Question

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

Answer 1

Call the short leg a.  The Pythagorean Theorem says:

$a^2 + (8 + 2 a)^2 = 52^2$

$a^2 + 8^2 + 32 a + 4a^2 = 52^2$

$5a^2 + 32 a + 8^2-52^2 = 0$

$5a^2 + 32 a + (8-52)(8+52) = 0$

$5a^2 + 32 a - (44)(60) = 0$

$(5a + 132)(a - 20) = 0$

Only the positive root $a=20$ is relevant here.

The other side is $2a+8=48$

The perimeter is $20 + 48 + 52 = 120$ inches