SOLUTION: A square chicken pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides in feet of each pen if the sides of the triangular pen are fi

Question 129436: A square chicken pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides in feet of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the length of each side of the square chicken pen be x.
Let the length of each side of the equilateral triangular pen be y.
From the problem description, you can write:
y = 2x-15 "...the sides of the triangular pen are fifteen less than twice a side of the square pen."
The problem also states that the perimeters of the two pens are equal.
The perimeter of the square pen can be written:

The perimeter of the triangular pen can be written:

Since the perimeters are equal, you can write:
or...
Substitute y = 2x-15
Simplify and solve for x.
Subtract 4x from both sides.
Now add 45 to both sides.
Divide both sides by 2.
ft.
Substitute x = 22.5

ft.
The length of each side of the square pen is 22.5 feet.
The length of each side of the triangular pen is 30 feet.
Check:
The perimeter of the square pen:

feet.
The perimeter of the triangular pen:

feet.
The perimeters are equal so the solution is correct!
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