short leg: x
long leg: 5x + 19
hypotenuse: 5x + 20
(short leg)² + (long leg)² = hypotenuse
(x)² + (5x + 19)² = (5x + 20)²
x² + 25x² + 190x + 361 = 25x² + 200x + 400
x² - 10x - 39 = 0 subtracted 25x², 200x, and 400 from both sides
(x - 13)(x + 3) = 0
x - 13 = 0 , x + 3 = 0
x = 13 x = -3 length cannot be negative so disregard -3
long leg: 5x + 19 = 5(13) + 19 = 65 + 19 = 84
hypotenuse: 5x + 20 = 5(13) + 20 = 65 + 20 = 85
Answer: short leg = 13, long leg = 84, hypotenuse = 85
