Problema Solution

In a right triangle, one leg is 3 more than the other, and the hypotenuse is 3 less than twice the shorter leg. find the numerical value of the perimeter of this triangle.

Answer provided by our tutors

Length of legs = x, y

Length of hypoteneuse = z

y = x+3  so y^2 = x^2 + 6x + 9

z = 2x-3 so z^2 = 4x^2 -12x +9

Substitute into Pythagoras's theorem: x^2 + y^2 = z^2  to get x^2 + x^2 + 6x + 9 = 4x^2-12x+9

which simplifies to 2x^2 -6x = 0

which has solution x=3

Therefore x+y+z = x+x+3+2x-3 = 4x = 12