How to find the perimeter of other polygons

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ISEE Upper Level Quantitative Reasoning › How to find the perimeter of other polygons

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If the perimeter of a septagon is equal to $5(x^{2}+1)+2x(x-4)$ , what is the length of one side? (All sides of the septagon are equal.)

$x^{2}-\frac{8x}{7}+\frac{5}{7}$

$7x^{2}+1$

$x^{2}-4x+5$

$7x^{2}-4x+5$

Explanation

If the perimeter of a septagon (in which all sides are equal) is $5(x^{2}+1)+2x(x-4)$ , then the length of one side will be one seventh of this expression.

To find one seventh, the value must first be simplified and then divided by 7.

$5(x^{2}+1)+2x(x-4)$

$5x^{2}+5+2x^{2}-8x$

$7x^{2}-8x+5$

When this is divided by 7, the result is:

$x^{2}-\frac{8x}{7}+\frac{5}{7}$

This value is thus the length of one side of the septagon.

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