Question

# A square animal pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are 15 less than twice a side of the square pen. (Hint: An equilateral triangle has three sides the same length.)

Solution

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Let $x$ be the side length of the square so that the side length of an equilateral triangle is $2x-15$.

We are given that the perimeters are equal so we write:

$P_{square}=P_{triangle}$

$4(x)=3(2x-15)$

Solve for $x$:

$4x=6x-45$

$-2x=-45$

$x=22.5$

So, the side length of the square pen is 22.5 and the side length of the triangular pen is $2(22.5)-15=30$.

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