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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.

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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 $\sqrt{(3x)^2 + (2x^2)} = \sqrt{13}x$

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