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

The perimeter of the triangle is `120` cm.

Explanation:

Let hypotenuse of the right triangle be `h=52`in.
One leg of the right triangle be `l_1`in.
Other leg of the right triangle be `l_2=2*l_1+8`in.
We know `h^2 = l_1^2+l_2^2 or 52^2=l_1^2+(2l_1+8)^2 or 2704 = l_1^2+4l_1^2+32l_1+64 or 5l_1^2+32l_1-2640=0`. This is a quadratic eqqution of which `a=5;b=32;c=-2640 ; l_1= (-32+-sqrt(32^2-4*5*(-2640)))/(2*5) or l_1=20.0 or l_1= -26.4` Length can not be negative number. So `l_1=20 ; l_2=2*20+8=48 ;h =52`
The perimeter of the triangle is `P= l_1+l_2+h=20+48+52=120`cm [Ans]