Step-by-step explanation:
let the longer leg = x
The shorter leg = 9cm shorter than the longer leg
The shorter leg = x - 9
hypotenuse = 9cm longer than the longer leg
hypotenuse = x + 9
Using pythagoras theorem:
hypotenuse² = shorter leg² + longer leg²
(x + 9)² = x² + (x - 9)²
Expanding:
x² + 9x + 9x + 81 = x² + x ² - 9x -9x + 81
x² + 18x + 81 = 2x² -18x + 81
collect like terms:
18x + 18x + 81 - 81 = 2x² - x²
36x + 0 = x²
x² - 36x = 0
x(x - 36) = 0
x = 0 or (x - 36) = 0
x = 0 or x = 36
if x = 0
shorter side = x - 9 = 0 - 9 = -9
Since the length cannot be negative, x = 36
The longer leg = x = 36 cm
The shorter leg = x - 9 = 36 - 9
The shorter leg = 27cm
The hypotenuse = x + 9 = 36 + 9
The hypotenuse = 45 cm