# The hypotenuse of a right triangle is 7 inches longer than the base and 14 inches longer than the height. the permeter of the triangle is 84 inches. find its area

To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following: Hypotenuse = 7 + base = 14 + height Perimeter = 84 inches The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So, Perimeter = height + base + hypotenuse = 84 We let x = height and y = base. We calculate area as follows: 84 = x + y + (7 + y) 77 = x + 2y x = 77 -2y Hypotenuse is related to the other sides by the Pythagorean theorem. Hypotenuse^2 = (x^2 + y^2) (14 + x)^2 = x^2 + y^2 (14 + (77-2y))^2 = (77-2y)^2 + y^2 (91-2y)^2 = (77-2y)^2 + y^2 Solving for y and x y = 28 x = 21 Area = (28)(21) / 2 = 294 square inches