(b) 240
step-by-step explanation:
first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.
pythagorean theorem formula:
a^2 + b^2 = c^2
(x - 20)^2 + (x - 40)^2 = x^2
x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2
x^2 -120x + 2000 = 0
(x - 100)(x - 20) = 0
x - 100 = 0 or x - 20 = 0
x = 100 or x = 20
we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.
perimeter = sum of the lengths of the sides
perimeter = x + x - 20 + x - 40
perimeter = 3x - 60
replace x with 100.
perimeter = 3(100) - 60
perimeter = 300 - 60
perimeter = 240
