Question

The hypotenuse of a right triangle is 10cm long. One of the triangle's legs is three times the length of the other leg. Find the lengths of the three sides of the triangle. In case of non-integer answer(s), round your answer(s) to the nearest hundredth.

Answer 1

The lengths of the three sides of the triangle are;

Hypotenuse = 10 cm

First leg = 3.162 cm

Second leg = 9.486 cm

Further Explanation:

Right triangle

• A right triangle is a triangle with one of its angles being 90 degrees or right angle.
• The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.

Pythagoras Rule

• According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.

• That is;$a^{2} +b^{2} =c^{2}$ , where a and b are the shorter sides while c is the hypotenuse.

In this case;

We are given;

Hypotenuse = 10 cm

First leg = $x cm$

second leg = $3x cm$

Therefore;

a = x cm

b = 3x cm

c = 10 cm

Hence;

$x^{2} +(3x)^{2} =10^{2}$

$x^{2} + 9x^2 = 100$

$x^{2} + 9x^2 =100$

Solving for x

$10x^{2} =100\\x^{2}=10\\x = \sqrt{10} \\x= 3.162$

Therefore;

x = 3.162 cm

hence;

The lengths of the three sides of the triangle are;

Hypotenuse = 10 cm

First leg = 3.162 cm

Second leg = 9.486 cm

Keywords: Right triangle, Pythagoras rule

Learn more about:

• Pythagoras theorem: brainly.com/question/4098846
• Right triangle: brainly.com/question/4098846

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem

Answer 2

Answer:

The lengths of the three sides are 10 cm, 9.49 cm and 3.16 cm

Step-by-step explanation:

Let

c ------> the length of the hypotenuse of a right triangle

x -----> the length of one leg

y -----> the length of the other leg

we know that

$c^{2}=x^{2}+y^{2}$ -----> equation A (Pythagoras Theorem)

$c=10\ cm$ ----> equation B

$x=3y$ -----> equation C

Substitute equation B and equation C in equation A and solve for y

$10^{2}=(3y)^{2}+y^{2}$

$100=10y^{2}$

$y^{2}=10$

$y=\sqrt{10}\ cm$

$y=3.16\ cm$

Find the value of x

$x=3(\sqrt{10})=9.49\ cm$

therefore

The lengths of the three sides are 10 cm, 9.49 cm and 3.16 cm