Question

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle?

Answer 1

c=52, a=2b+8
a^2+b^2=c^2
(2b+8)^2+b^2=52^2
4b^2+32b+64+b^2=2704
5b^2+32b-2640=0 see below
b=20, a=48
48+20+52
=120"

Answer 2

Answer: 120 in.

Step-by-step explanation:

Given: The hypotenuse of a right triangle is 52 in.

Let the length of one leg be x, then the length of other leg will be 2x+8

By Pythagoras theorem of right triangle, we have

$52^2=x^2+(2x+8)^2\\\\\Rightarrow\ 2704=x^2+4x^2+32x+64\\\\\Rightarrow\ 2704=5x^2+32x+64\\\\\Rightarrow\5x^2+32x-2640=0\\\\\Rightarrow\ (x-20)(5x+132)\\\\\Rightarrow\ x=20\ or\ x=\dfrac{-132}{5}\ \ \ \text{[side cannot be negative]}\\\\\Rightarrow\ x=20$

Perimeter of triangle will be:

$52+x+(2x+4)\\\\=52+20+(2(20)+8)\\\\=120\text{ in.}$

• Pythagoras theorem of right triangle says that the square of the hypotenuse  is equal to the sum of the squares of the other two sides.