Question

The hypotenuse of a right triangles is 7 inches longer than the base and 14 inches longer than the height. The perimeter is 84 inches. Find its area

Answer 1

294 in^2 = A

Explanation:

Let h represent the length of the hypotenuse, b the base and h the height. Because this is a right triangle, the Pythagorean Theorem applies.

(hypotenuse)^2 = (base)^2 + (height)^2

h^2 = (h - 7)^2 + (h - 14)^2

Perimeter of the triangle is 84 inches, equal to (h) + (h - 7) + (h - 14), which in turn simplifies to 84 = h + h - 7 + h - 14, or 84 = 3h - 21, or 3h = 105. Solving this for h, we get h = 35.

Then the base is (35 - 7), or 28, and the height is (35 - 14), or 21.

The area of the triangle is found using the formula

A = (1/2)(base)(height) = (1/2)(28)(21) = 294 in^2 = A