Question 1169604: Cara has a piece of wire. She bent the wire into square and then bent it into an equilateral triangle. She found that the length of a side of the square is 5 cm shorter than that of the equilateral triangle.Find the length of a piece of wire.
Answer by math_tutor2020(3816)   (Show Source):
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L = length of wire in cm
A square has 4 sides that are all equal, so each side is L/4 cm long.
An equilateral triangle has all 3 sides equal, so each side is L/3 cm long.
We're told that "the length of a side of the square is 5 cm shorter than that of the equilateral triangle" so,
(side length of square) = (side length of triangle) - 5
L/4 = L/3 - 5
12*(L/4) = 12*(L/3 - 5)
3L = 4L - 60
3L-4L = -60
-L = -60
L = 60
In the third step shown above, I multiplied both sides by the LCD 12 to clear out the fractions
The length of the wire is L = 60 cm.
The square side length is L/4 = 60/4 = 15 cm.
The equilateral triangle side length is L/3 = 60/3 = 20 cm.
We see that the square's side length is 5 cm shorter compared to the triangle. This confirms our answer.
Answer: The wire is 60 cm long.
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