How to find the length of the side of other quadrilaterals

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ISEE Upper Level Quantitative Reasoning › How to find the length of the side of other quadrilaterals

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The perimeter of a quadrilateral is 86. The four sides measure

$15,25,30,\textup{ and }\left ( 2x^{2}\cdot \frac{2}{x}\right )$ .

What is the value of ?

Given that the perimeter is 86, the sides of the quadrilateral will all add up to this amount.

$15+25+30+2x^{2}\cdot \frac{2}{x}=86$

The first step is the add together all the integers.

$70+2x^{2}\cdot \frac{2}{x}=96$

Next, we subtract 70 from each side.

$2x^{2}\cdot \frac{2}{x}=16$

We reduce the left side of the equation:

Now, we divide each side by 4. This leaves: