SOLUTION: If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2, what were the dimensions of the original square?
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-> SOLUTION: If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2, what were the dimensions of the original square?
I am very much stuck, how do I do this?
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Question 84570This question is from textbook algebra
: If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2, what were the dimensions of the original square?
I am very much stuck, how do I do this? This question is from textbook algebra
You can put this solution on YOUR website! Let x represent the length of the side of a square.
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Therefore, the area (A) of this square is given by the equation:
.
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Shorten the length of the side of the square by 2 cm. This means that the length of the side
is now cm.
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The area of this new square is given by the equation:
.
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The difference of this area and the area of the original square is 36 cm^2. In equation
form this becomes:
.
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This reduces the equation to:
.
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Get rid of the -4 on the left side by adding +4 to both sides:
.
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Solve for x by dividing both sides by 4 which is the multiplier of x. This division
results in:
.
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Since x was the side of the original square, we can now say that the side of the original
square was 10 cm in length.
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Check. The area of the original square would be 10 times 10 or 100 square cm. Shortening
the sides by 2 cm would make the sides of the new square 8 cm in length. The area of
the new square would be 8 times 8 or 64 square cm. The difference between the 100 square
cm area and the 64 square cm area is 36 square cm, just as the problem asked for it to be.
This indicates that the answer of 10 cm as the length of a side of the original square is
correct.
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Hope this explanation helps you to work your way through the problem
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