1985 AJHSME Problems/Problem 19
Problem
If the length and width of a rectangle are each increased by , then the perimeter of the rectangle is increased by
Solution #1
Let the width be and the length be . Then, the original perimeter is .
After the increase, the new width and new length are and , so the new perimeter is .
Therefore, the percent change is
Solution #2 (Quick Fakesolve)
Assume WLOG that the rectangle is a square with length and width . Thus, the square has a perimeter of . Increasing the length and width by will increase the dimensions of the square to 11x11. Thus, the new square's perimeter is , and because is of , our answer is .
See Also
1985 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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