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Question 1167840: A square and an equilateral triangle have the same perimeter. The area of the square is 13 more than the length of a side of the triangle. What is the length of a side in the triangle (in inches)? What is the area of the square (in square inches)?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! side of triangle is s
perimeter is 3s
so side of square is 0.75 s for perimeter of 3s
The square's area is 0.5625 s^2 and that is 13 more than area of triangle.
the area of an equilateral triangle is (1/2)(s)*(s/2)(sqrt(3)=(1/4)s^2(sqrt(3)
therefore (9/16)s^2-13=sqrt(3)/4 s^2, converting to fractional form
or (9/16)s^2-13=4 sqrt(3)s^2/16
and 9s^2-208=4 sqrt(3)s^2
[9-4 sqrt(3)]s^2=208
2.072 s^2=208
s^2=208/(9-4 sqrt(3))
s=10.02 inches, side of the triangle; side of square is 7.51 inches
Check this.
A square is 56.47 in^2 (I didn't round until the last step)
side of triangle is 10.02 in.
altitude is 5.01*sqrt(3) in=8.68 inches
Area of triangle is 43.47 in^2,
The answer is 10.02 inches for the triangle and 56.47 in^2 for the square
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