Problem:
If the length of a rectangle is increased by and its width is increased by , then the area is increased by
Answer Choices:
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Solution:
When a problem indicates a general result, then it must hold for any specific case. Therefore, suppose the original rectangle is by with area . The new length is and the new width is . Hence the new area is for an increase of .
The length is changed to times its original value, and the width is changed to , or times its original value. Since area is length times width, the new area is times the original area. Thus the area is increased by .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions