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 

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