The longer leg of a right triangle is 7 cm longer than the shorter leg. the hypotenuse is 8 cm longer than the shorter leg. what is the perimeter of the triangle?

First we define a variable:

x: length of the shortest side of the triangle.

Then, using the Pythagorean theorem we have:

(x + 8) ^ 2 = x ^ 2 + (x + 7) ^ 2

Rewriting we have:

x ^ 2 + 16x + 64 = x ^ 2 + x ^ 2 + 14x + 49

Clearing x we have:

64 - 49 = 2x ^ 2 - x ^ 2 + 14x - 16x

64 - 49 = 2x ^ 2 - x ^ 2 + 14x - 16x

15 = x ^ 2 - 2x

x ^ 2 - 2x - 15 = 0

The roots of the polynomial are:

x = - 3

x = 5

We discard the negative root because it is a dimension.

Then, the perimeter is:

P = (x + 7) + (x + 8) + x

P = (5 + 7) + (5 + 8) + 5

P = 30

Answer:

the perimeter of the triangle is:

P = 30