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A rectangular piece of plywood is trimmed to make a square by cutting a 4-cm
strip off the top and a 2-cm strip off one side.
If the area of the original piece is 74 cm2 greater than the area of the
square, find the dimensions of the rectangle.
Let L = length of the rectangle
Let W = width of the rectangle
then draw a diagram and it will be apparent that:
(W-2) = side of the square
(L-4) = side of the square
W - 2 = L - 4
W = L - 4 + 2
W = (L-2)
"If the area of the original piece is 74 cm2 greater than the area of the square, find the dimensions of the rectangle."
L * W = 74
Replace W with (L-2)
L*(L-2) = 74
L^2 - 2L - 74 = 0
We have to use the quadratic equation to solve this:
In this problem: x=L; a=1; b=-2; c=-74
L = 9.66 cm is the length of the rectangle
W = 9.66 - 2 = 7.66 cm is the width of the rectangle
Check solution by finding the area using these values:
9.66 * 7.66 = 73.9975 ~ 74; confirms our solution