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

Question 334477: The hypotenuse of a right triangle is 7 inches longer than the base and 14 inches longer than the height. The perimeter of the triangle is 84 inches. Find its area.
Found 2 solutions by mananth, solver91311:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let hypotenuse be x
side 1 = x-7
side 2 = x-14
..
x+x-7+x-14=84
3x-21=84
add 21
3x-21+21=84+21
3x=105
divide by 3
x= 35
..
base = 35-7= 28
height = 35-14= 21
..
Area = 1/2 * 21*28
=21*14
=294 sq. inches
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the measure of the hypotenuse. Then represents the measure of the base and represents the measure of the height. The perimeter is the sum of the three sides, so:

Solve for to get the hypotenuse, subtract 7 to get the measure of the base, subtract 14 to get the measure of the height, multiply the base times the height and divide by 2.

John

My calculator said it, I believe it, that settles it

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