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?

1 Answer
Dec 1, 2016

The perimeter of the triangle is 120 cm.

Explanation:

Let hypotenuse of the right triangle be h=52in.
One leg of the right triangle be l1in.
Other leg of the right triangle be l2=2l1+8in.
We know h2=l21+l22or522=l21+(2l1+8)2or2704=l21+4l21+32l1+64or5l21+32l12640=0. This is a quadratic eqqution of which a=5;b=32;c=2640;l1=32±32245(2640)25orl1=20.0orl1=26.4 Length can not be negative number. So l1=20;l2=220+8=48;h=52
The perimeter of the triangle is P=l1+l2+h=20+48+52=120cm [Ans]