Answer:
Shorter leg = 20 cm.
Longer leg = 21cm.
Hypotenuse = 29 cm
Step-by-step explanation:
Let the shorter leg be x cm long
Then longer leg = x + 1 and hypotenuse = x + 9 cm long
So by Pythagoras:
x^2 + (x + 1)^2 = (x + 9)^2
0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)
x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0
-x^2 + 16x + 80 = 0
x^2 - 16x - 80 = 0
(x - 20)(x + 4) = 0
So x = 20 (we ignore the negative root).
So longer leg = 20 + 1 and hypotenuse = 20 + 9.
