The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one decimal place.

Answers

Answer 1

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

[tex]x + 2 \text{ cm}[/tex]

According to the Pythagorean Theorem, for a right triangle:

[tex]a^2 + b^2 = c^2[/tex]

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

[tex](x)^2 + (x+2)^2 = 6^2[/tex]

Solve for x. Simplify:

[tex]x^2 + (x^2 + 4x + 4) = 36[/tex]

Simplify:

[tex]2x^2 + 4x + 4 = 36[/tex]

Subtract:

[tex]2x^2 + 4x - 32 =0[/tex]

Divide:

[tex]x^2 + 2x - 16 = 0[/tex]

The equation is not factorable, so we can consider using the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]

In this case, a = 1, b = 2, and c = -16. Substitute:

[tex]\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}[/tex]

And evaluate:

[tex]\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}[/tex]

Hence, our two solutions are:

[tex]\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1[/tex]

Lengths cannot be negative, so we can ignore the second solution.

Hence, the value of x or the first side length is about 3.1 centimeters.

Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.

In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.


Related Questions

Which of the following angles is coterminal with -59˚? *

A. 2700˚
B. B. 301˚
C. C. 550˚

Answers

Answer:  B) 301 degrees

===============================================================

Explanation:

To find a coterminal angle, we add on 360 degrees

-59+360 = 301

The angles -59 degrees and 301 degrees point in the same exact direction. This is why they are coterminal.

Please can you solve this questions for me!!
It's important ​

Answers

15:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{x^5y^6}{xy^2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{5-1}y^{6-2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^4y^4[/tex]

16:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{x^2y^5}{xy^4}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{2-1}y^{5-4}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto xy[/tex]

17;-

[tex]\\ \qquad\quad\sf\longmapsto \left(\dfrac{4x^5y}{16xy^4}\right)^3[/tex]

[tex]\\ \qquad\quad\sf\longmapsto (4^{1-2}x^{5-1}y^{1-4})^3[/tex]

[tex]\\ \qquad\quad\sf\longmapsto (4^{-1}x^4y^{-3})^3[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 4^{-3}x^{12}y^{-9}[/tex]

18:-

[tex]\\ \qquad\quad\sf\longmapsto \left(\dfrac{5x^3y}{20xy^5}\right)^4[/tex]

[tex]\\ \qquad\quad\sf\longmapsto (4^{-1}x^{2}y^{-4})^4[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 4^{-4}x^8y^{-16}[/tex]

19:-

[tex]\\ \qquad\quad\sf\longmapsto y^{-7}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{y^7}[/tex]

20:-

[tex]\\ \qquad\quad\sf\longmapsto 7^{-2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{7^2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{49}[/tex]

21:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{x^{-5}}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^5[/tex]

22:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{2^{-4}}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2^4[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 16[/tex]

23:-

[tex]\\ \qquad\quad\sf\longmapsto x^5\times x^{-1}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{5-1}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^4[/tex]

24:-.

[tex]\\ \qquad\quad\sf\longmapsto x^{-6}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{x^6}[/tex]

25:-

[tex]\\ \qquad\quad\sf\longmapsto x^9(x^{-7})[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{9-7}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^2[/tex]

Solve the equation for Y. Then find the value of y for each value of X.

y+2x=5;x=-2,0,4

help me on this pls

Answers

Answer:

y=5-2x

2 5-2(2)=5-4=1

0 5-2(0)=5

4 5-2(4)=5-8=-3

What is 1,025 divided by 68 full explanation

Answers

Answer:

15.1 (rounded to the nearest tenth decimal point)

Step-by-step explanation:

The explanation is, this is simple maths, nothing else. Let me know if it helps. Thank you

The answer to 1025 divided by 68 is 15.07

this one is for the math experts!
Please help and get it correct for a chance to get brainly!

Answers

Answer:

-52

Step-by-step explanation:

i think its -52 i don't know this. just a guess not being rude<3

Answer:

-52 has a greater value

|-52| = 52

............

Mr.ford drove 224 miles in 4 hours. At what rate of speed did he drive?

Answers

Answer:

56 miles per hour i think

Step-by-step explanation:

PLEASE HELP FAST!! I CANNOT GET THIS WRONG!!!!
Makayla and David work at a furniture store. Makayla is paid $230 per week plus 7.5% of her total sales in dollars, x, which can be represented by g(x)=230+0.075x. David is paid $321 per week plus 4% of his total sales in dollars, x, which can be represented by f(x)=321+0.04x. Determine the value of x, in dollars, that will make their weekly pay the same.

Answers

Answer:

6

Step-by-step explanation:

you kna mean?

How is constructing an angle bisector similar to constructing a perpendicular bisector?
A. Both constructions begin with a given angle
B. Both constructions allow you to find the midpoint of a segment.
C. Both constructions require that you draw a ray.
D. Both constructions require the point where two arcs intersect.

Answers

Answer:

D. Both constructions require the point where two arcs intersect.

Step-by-step explanation:

D is your answer

Both constructions require the point where two arcs intersect. Then the correct option is D.

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Building an angle bisector is similar to building a perpendicular bisector in that both constructs call for the intersection of two arcs.

Angle bisector means dividing an angle into two equal parts. And the perpendicular bisector means the line is divided into two equal line segments.

Both constructions require the point where two arcs intersect.

Then the correct option is D.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

23° is equal to
1
23
01
23

Answers

Step-by-step explanation:

I am sure there is something missing or horribly mistyped.

if you really meant 23⁰, then that is 1.

whats number 26.




..............................

Answers

Answer:

y = 1/3mx + b

Step-by-step explanation:

x = 3(y - b)/m

~Multiply m to both sides

mx = -3b + 3y

~Add 3b to both sides

mx + 3b = 3y

~Divide everything by 3

1/3mx + b = y

y = 1/3mx + b

Best of Luck!

[tex]\\ \rm\longmapsto x=\dfrac{3(y-b)}{m}[/tex]

[tex]\\ \rm\longmapsto mx=3(y-b)[/tex]

[tex]\\ \rm\longmapsto mx=3y-3b[/tex]

[tex]\\ \rm\longmapsto 3y=mx+3b[/tex]

[tex]\\ \rm\longmapsto y=\dfrac{1}{3}mx+b[/tex]

bobby's mom gets a small pot of water on the stove and lights a burner. ten minutes later, bobby notices small bubbles and sees that the water is almost boiling. which of the following could possibly be the tempeture of the water in the pot.
a 120F
b 95 C
c 99 F
d 110 C

Answers

B would be the answer i hope i am correct and also if you could make me brainiest that would be great!

PLEASE HELP! 10 points!​

Answers

Step-by-step explanation:

It easy isn't it my friend

wats 10 to the 2nd power divied by 5 to the 2nd power

Answers

Answer:

4

Step-by-step explanation:

10^2/5^2

Do the exponents first

10 to the 2nd power is 100

5 to the 2nd power is 25

100/25

100 divided by 25 is 4

So the answer is 4

Hope this helps!

please help ill mark brainliest

Answers

Answer:

AED = 136

Step-by-step explanation:

plz mark me as a brainlist

Find the slope of the line with points (-3, -8) and (-3, 5)

Answers

Step-by-step explanation:

let ,(-3,-8)=(X2,y2)

(-3,5) =(x1,y1)

then

slope (M) =

[tex](y2 - y1 ) \div x2 - x1)[/tex]

={(-8)-5 }÷{(-3)-(-3)}

= -13÷ 0

=0

m²+16m=4 give the number that must be added to both side​

Answers

this is correct solution thank you

Is √5x - 12 = 0 nonlinear or linear?

Answers

Nonlinear because in order to be linear, it has to be a straight line. In order to be a straight line, the degree must be 0 or 1 for each of its variables. This does not meet that criteria, thus being non linear

There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 197 inches? Enter the answer in the box.
meters

Answers

Answer:

5 meters

Step-by-step explanation:

If in 1 inch have 2.54 centimeters, in 197 inches will have:

197×2.54 = 500.38 centimeters

If 100 centimeters are 1 meter, 500 centimeters will have 5 meters, so 197 inches have 5 meters

PLEASE HELP!!! HIGHSCHOOL GEOMETRY
(05.03 MC)
In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF, while point E is the point of intersection between segment DG and segment BF.

Prove ΔABC ∼ ΔGEC. (10 points)

Answers

Step-by-step explanation:

ABC is congruent to DEF because angle C = angle C because of vertical angles angle E = angle E because of vertical angles angle G = angles A and D because of 3rd angle theorem triangle ABC ~ triangle GEC because of congruent angles.

A car is traveling at 55 mph. What is the
speed of the car in feet per second (ft/s)?

Answers

Answer:

80 feet per second

Step-by-step explanation: At 55 mph, your vehicle is traveling at about 80 feet per second. Feet-per-second is determined by multiplying speed in miles-per-hour by 1.47 (55 mph x 1.47 = 80 feet per second.)

80 feet’s per second . !

If you vertically stretch the exponential function f(x)= 2^x by the factor of 4, what is the equation of the new function

Answers

Answer:

to vertically strech a function by a factor of c, multiply the whole function by c

so

f(x) vertically streched by a factor of 4 is 4f(x)

so we get

the new function is f(x)=4(2)ˣ

Step-by-step explanation:

24 - 8X = -16
Help pls

Answers

Answer:

5

Step-by-step explanation:

24-8X=-16

24+16=8X

40=8X

X=5

Answer:

x=5

Step-by-step explanation:

24 - 8x = -16

=> 24 + 16 = 8x

=> 8x = 24 + 16

=> 8x = 40

=> x = 40/8

=> x = 5

If f(x) = x^2 + 8x – 2 and f(0), then the result is:

-2.
0.
8.

Answers

Answer:

-2.

Step-by-step explanation:

f(0) = 0^2 + 8(0) - 2

= -2.

48 ounces of liquid detergent
for $6.19. Find the unit rate

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

Around 13 cents.

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\rightarrow \frac{dollars}{ounces}= \frac{6.19}{48}=\frac{6.19/48}{48/48}=0.128958... \approx \$0.13[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Please help :)
Please explain your answer also because I need to learn this!

A paratrooper and counter stronger winds than anticipated while parachuting from 1350 feet, causing him to drift at an 8° angle. How far from the drop zone will the paratrooper land? ​

Answers

Answer:

189 feet

Step-by-step explanation:

the distance from the drop zone the paratrooper will land = h × tan 8°

= 1350 × 0.14 = 189 feet

Is KV=21, what does OZ=

Please help

Answers

Answer:

OZ = 23

Step-by-step explanation:

32 divided by 752.4 help me pppplease

Answers

Answer:

0.0425

Step-by-step explanation:

just use a calculator

What percentage of Americans would you predict wear contact lenses?​

Answers

About 11% of Americans wear contacts!

The sum of two consecutive even integers is 214. What are the integers?

Answers

Answer:

Let the numbers be a and a + 2

According to question,

a + a + 2 = 214

=> 2a + 2 = 214

=> 2a = 212

=> a = 106

First number = 106

Second number = 108

Step-by-step explanation:

plz mark me brainliest

Answer:

106, 108

Step-by-step explanation:

even numbers

say n, n+2

n+n+2=214

2n=212

n=212/2=106

even numbers are 106 and 108

Need help with 10 and 11

Answers

Answer:

10: A  11: B i think

Step-by-step explanation:

Answer:

A. (1,5.5)B. 11 units

[tex]\small\bold\color{gray}{\colorbox{white}{√CarryOnLearning}}[/tex]

(ノ^_^)ノ

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