Question

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Answer 1

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