SOLUTION: Geomatry. If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2

Question 92555: Geomatry. If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let x be the length of the side of the original square. Therefore, the area of the original
square is x^2.
.
Now take 2 cm off each side of the original square. That means that the length of the side
of the new square is x-2 cm. You square this to get the area of this new square. So the
area of the new square is:
.

.
The problem then says that the difference between the original area and the new
area is 36 cm^2. Setting this up as an equation we have:
.

.
Since the parentheses are preceded by a minus sign, you can remove the parentheses
by changing the signs of the terms within the parentheses. This leads to:
.

.
Note that the terms cancel each other due to their difference in signs. So
they drop from the equation which then becomes:
.

.
Get rid of the -4 on the left side by adding +4 to both sides. This reduces the equation to:
.

.
Solve for x by dividing both sides by 4 to get:
.

.
So the length of each side of the original square is 10 cm.
.
And the length of each side of the new square is 10 - 2 or 8 cm.
.
Check. The area of the original square is 10*10 = 100 cm^2. The area of the new square is
8 * 8 = 64 cm^2.
.
The difference in their areas is 100 cm^2 - 36 cm^2 = 64 cm^2.
.
Hope that the answer you were looking for is in here somewhere. This will probably
give you the process you can use to solve this problem.
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