# Trapezoid problem

A trapezoid in which the lengths of the two sides that are not parallel are equal. The length of the longer parallel side is $$5$$ times the length of the shorter parallel side, and the distance between the two parallel side is $$3$$ times the length of the shorter parallel side. The perimeter of the trapezoid is $$135$$ meters. Approximately what is the length, in meters, of the shorter parallel side?

I'm stuck on this question, not sure what I missed.

I can let the shorter side equal to $$x$$ so the longer side is $$5x$$ and two equal side is $$2y$$, sum up $$6x + 2y = 135$$ not sure what I can do from here to go further, and the area is obviously $$\frac{6x \times 3x}{2} = 9x^2$$ The answer is $$10$$, any suggestions to help me to approach would be highly appreciated.

Can you show that $$y = \sqrt{13}x$$ and solve for $$x?$$
Draw a perpendicular to the longer side from one end of the shorter side and consider the right angled triangle formed. It has two shorter sides of length $$3x$$ and $$2x$$. Hence the length of the hypotenuse $$y$$ must be $$\sqrt{(3x)^2 + (2x^2)} = \sqrt{13}x$$