Question 181580: a rectangle garden is ten m longer than it is wide. the owner wants to increase the size of the garden. if he adds an additional 3m to each of the four sides, he will gain an additional 216 m squared of the garden area. what are the dimensions of the garden?
i just dont get these. my teacher has tried to explainthem to me multiple times. i just cant seem to get past writing the first part : x+10 and x and then the bigger one's x+13 and x. help?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You have the original dimensions correct, namely x and x + 10. But Mr. Gardener wants to add 3 meters to each side of the garden. That means 3 meters on the top, 3 on the bottom, 3 on the left, and 3 on the right.
That means that the new dimensions are x + 3 + 3 = x + 6 and x + 10 + 3 + 3 = x + 16.
The added area is 216 square meters, which would be the area of the new, larger garden, given by (x + 6)) minus the area of the original garden, given by (x)) . Think of it as a rectangular sheet of paper which has an area that is the length times the width, then you cut a rectangular hole in the center of it, subtracting an area that is the length times the width of the hole, leaving you with a picture frame looking thing.
So, putting it all together, you can say:
The area of the new garden minus the area of the old garden is 216 square meters. Symbolically stated:
(x + 6)\right]-\left[(x + 10)(x)\right] = 216) .
So multiply using FOIL and the distributive property and collect all like terms, leaving the 216 on the right. The result will be a simple single variable linear equation that can be solved for the value of x.
John
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