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 xx be the side length of the square so that the side length of an equilateral triangle is 2x152x-15.

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

Psquare=PtriangleP_{square}=P_{triangle}

4(x)=3(2x15)4(x)=3(2x-15)

Solve for xx:

4x=6x454x=6x-45

2x=45-2x=-45

x=22.5x=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=302(22.5)-15=30.

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