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