I need help solving this math question please

Question

On a right triangle, I need one leg to be 7 meters longer than the other leg, and need the hypotenuse to be 1 meter longer than the longer leg. To do this I need to know the perimeter and the area of the triangle. So what is the length of each leg on triangle? What is the perimeter of the triangle? What is the area of the triangle?

Answer 1

Hi, Bryant!

First start drawing the question:

short leg is x

long leg is x+7

hypotenuse is x+8

Then, put it into Pythagorean:

(x+7)² + (x) ² = (x+8)²

Solve for x:

x= -3 and 5

-- In the context of this problem, a negative value would not work so 5 is x for this problem

Then plug 5 back into the value of the lengths:

5+7=12 for long leg

5 is shorter leg

5+8= 13 for hypotenuse

Area is bh x .5 so the base is 5 and height is 12

Parameter is all the lengths added together 13+ 12+ 5