Question

the hypotenuse of a right triangle is 20 centimeters. one of the legs is 4 cm longer than the other leg. find the area of the triangle.

Answer 1

hypotenuse = 20

leg = x + 4

other leg = x

From the Pythagorean Theorem we know that

20^2 = (x + 4)^2 + x^2

400 = x^2 + 8x + 16 + x^2

2 x^2 + 8x -384 = 0

Solving the quadratic equation we get

x = 12 and x = -16

x = 12 and so the lengths of the 2 legs are:

12 and 16

Right Triangle Area = (leg1 * leg2) / 2

Right Triangle Area = (12 * 16) / 2

Area = 192 / 2

Area = 96 square centimeters

Explanation: