Question 267174: If the side of a square is decreased by 3 meters, the area is decreased by 45 square meters. Find the length of the original square. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! Let x = length of the sides of the original square.
Then x-3 = the length of the side of the square after the sides have been decreased by 3
The area of any square is where s is the length of the sides. For the original square, since the length of the sides of the original square is x, the area would be . The area of the reduced square would be .
We are told that the area of the reduced square is 45 square meters less than the area of the original square. In other words, the area of the reduced square, , plus 45 equals the area of the original square. So
We now have an equation we can solve. We start by simplifying. (Remember to use FOIL or the pattern for (a-b)^2 on the left side. is not!)
Subtract form each side:
Subtract 54 from each side:
Divide both sides by -6:
Since x is the length of the side of the original square and since that is what the problem asks us to find, then the answer to the problem is 9.
If we want to check our answer we can find the side of the reduced square which is x-3 or 6. Then we can find the areas of the two squares: square meters square meters
The difference in these two areas is square meters. Check!
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