Question

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?

Answer 1

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