Question

If each side of a regular pentagon is X2 + 17 and each side of a regular hexagon is x2 + 2x, for what value or values of x will be the perimeters of the figures be equal

Answer 1

Just set the perimeteres equal:
5(x^2 +17) = 6(x^2 + 2x)
and solve the resulting quadratic.

x^2 +12x -85 = 0
(x + 17)(x-5) = 0
Negative x solutions are not of interest, so the answer is x=5