SOLUTION: 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 th
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Question 201058: 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.
Thanks for your help. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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
and
(L-4) = side of the square
Therefore
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
:
:
:
Positive solution
:
L = 9.66 cm is the length of the rectangle
then
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
