Question 998383: The perimeter of MNO is equal to the perimeter of square ABCD. If the lengths of the sides of the triangle are represented by 4x + 4, 5x - 3, and 17, and one side of the square is represented by 3x, find the length of a side of the square.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The perimeter of MNO is equal to the perimeter of square ABCD.
If the lengths of the sides of the triangle are represented by 4x + 4, 5x - 3, and 17,
and one side of the square is represented by 3x,
find the length of a side of the square.
:
Find the perimeter of the triangle
p = (4x+4) + (5x - 3) + 17
combine like terms
p = 9x + 4 - 3 + 17
p = 9x + 18
find the perimeter of the square
p = 4(3x)
p = 12x
perimeters are equal, therefore
12x = 9x + 18
12x - 9x = 18
3x = 18
x = 18/3
x = 6
find the length of the sides of the square
3(6) = 18
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Confirm this by finding the perimeters of each
the square:
4(18) = 72
the triangle
p = (4(6)+4) + (5(6) - 3) + 17
p = (24+4) + (30 - 3) + 17
p = 28 + 27 + 17
p = 72
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