One leg of a right triangle is 21 inches longer than the other leg, and the hypotenuse is 39 inches.

Find the lengths of the legs of the triangle

One leg - 15 inches

Second leg - 36 inches.

Step-by-step explanation:

One leg - x inches.

Second leg - (x + 21) inches.

Hypotenuse - 39 inches.

Using Pythagorean theorem

x² + (x + 21) ² = 39²

x² + x² + 2*21x + 21² = 39²

2x² + 42x - 39² + 21² = 0

2x² + 42x - 1080 = 0

x² + 21x - 540 = 0

(x - 15) (x + 36) = 0

x = 15, x = - 36

We can use only positive value.

One leg - x inches = 15 inches

Second leg - (x + 21) inches = 15+21=36 inches.