Question 39896This question is from textbook Beginning Algebra
: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm^2. What were the dimensions of the original square?
This question is from textbook Beginning Algebra
Found 2 solutions by checkley71, Fermat:
Answer by checkley71(8403)   (Show Source):
Answer by Fermat(136)  (Show Source):
You can put this solution on YOUR website! If what you have is a square, then both the sides have the same size.
Let the size of the square be x.
Then the area of the square is,
A = x * x = x^2
A = x^2
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The new sides of the square are now x-2.
The new area of the square is therefore,
A2 = (x-2) * (x-2) = (x-2)^2
A2 = (x-2)^2
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We are told that the new area, A2 is 36 cm^2 less than the original square. So we can write,
A2 = A - 36
Substituting for A = x^2 and A2 = (x-2)^2, we get
(x-2)^2 = x^2 - 36
now exand the brackets on the lhs,
x^2 - 4x + 4 = x^2 - 36
subtract x^2 from both sides,
-4x + 4 = -36
change the signs of all the terms,
4x - 4 = 36
add 4 to both sides,
4x = 40
divide both sides by 4,
x = 10 cm
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