SOLUTION: A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle. Find the area of the square, if it is known, that it

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Question 1011028: A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle. Find the area of the square, if it is known, that it is 50 cm2 smaller that the area of the rectangle.
Answer by ankor@dixie-net.com(22740) (Show Source):
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A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle.
Find the area of the square, if it is known, that it is 50 cm2 smaller that the area of the rectangle.
:
Let L = length of the rectangle
Let W = the width
:
"A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle."
All side of the square is equal, therefore
L - 5 = W + 2
L = W + 7
"The square is 50 cm2 smaller that the area of the rectangle."
L*W - (W+2)^2 = 50
Replace L with (w+7); FOIL (W+2)(W+2)
W(W+7) - (W^2 + 4W + 4) = 50
W^2 + 7W - W^2 - 4W - 4 = 50
Combine like terms
3W = 50 + 4
3W = 54
W = 54/3
W = 18 is the width of the rectangle
Then
18+2 = 20 cm is the side of the square
and
20^2 = 400 sq/cm is the area of the square