Answer:
Length of smaller side = 15 inches
Length of bigger side = 36 inches
Length of hypotenuse = 39 inches
Step-by-step explanation:
Given:
Length of smaller side = a
Length of bigger side = (a + 21) inches
Length of hypotenuse = (a + 24) inches
Find:
Length of all side
Computation:
Using Pythagorean theorem
Hypotenuse² = Base² + Perpendicular²
(a+24)² = a² + (a+21)²
a² + 576 + 48a = a² + a² + 441 + 42a
a² - 6a - 135 = 0
(a-15)(a+7)
So
a = 15 inches a = -7 inches
So,
Length of smaller side = a = 15 inches
Length of bigger side = (a + 21) inches = 15 + 21 = 36 inches
Length of hypotenuse = (a + 24) inches = 15 + 24 = 39 inches
