SOLUTION: the side of an equilateral triangle is 8 inches shorter than the side of a square. The perimeter of the square is 46 inches more than the perimeter of the triangle. Find the leng

Algebra ->  Triangles -> SOLUTION: the side of an equilateral triangle is 8 inches shorter than the side of a square. The perimeter of the square is 46 inches more than the perimeter of the triangle. Find the leng      Log On


   

Question 484021: the side of an equilateral triangle is 8 inches shorter than the side of a square. The perimeter of the square is 46 inches more than the perimeter of the triangle. Find the length of a side of the square.
Found 2 solutions by cleomenius, MathTherapy:
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
4x - 46 = 3(x + 8)
4x - 46 = 3x + 24
x = 70 inches
4(70) -46 = 234 = 78(3) = 234 inches
Cleomenius.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
the side of an equilateral triangle is 8 inches shorter than the side of a square. The perimeter of the square is 46 inches more than the perimeter of the triangle. Find the length of a side of the square.

Let each side of the square be S
Then each side of the triangle is S – 8
Perimeter of square is then: 4S, and perimeter of triangle is: 3(S – 8), or 3S - 24

Since perimeter of square is 46” more than the perimeter of the triangle, then we’ll have:

4S = (3S – 24) + 46
S = 22

S, or one side of square = highlight_green%2822%29"

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Perimeter of square, since one side is 22” is 88 (4 * 22)
Perimeter of triangle, since one side is 14” (22” – 8”) is 42 (3 * 14)

As seen, perimeter of square (88”) is 46” more than perimeter of triangle (42”), as 88” – 42” = 46”

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