Difference between revisions of "1999 AMC 8 Problems/Problem 5"
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| − | == | + | ==Problem== |
| − | A rectangular garden | + | A rectangular garden 60 feet long and 20 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden? |
| − | make the garden larger, while using the same fence, its shape is changed to a | ||
| − | square. By how many square feet does this enlarge the garden? | ||
| − | |||
| − | + | <math>\text{(A)}\ 100 \qquad \text{(B)}\ 200 \qquad \text{(C)}\ 300 \qquad \text{(D)}\ 400 \qquad \text{(E)}\ 500</math> | |
| − | + | ==Solution== | |
| − | + | ||
| − | + | We need the same perimeter as a 60 by 20 rectangle, but the greatest area we can get. right now the perimeter is 160. To get the greatest area while keeping a perimeter of 160, the sides should all be 40. that means an area of 1600. Right now, the area is 20 times 60 which is 1200. 1600-1200=400 which is D. | |
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==See Also== | ==See Also== | ||
{{AMC8 box|year=1999|num-b=4|num-a=6}} | {{AMC8 box|year=1999|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Revision as of 11:05, 23 November 2020
Problem
A rectangular garden 60 feet long and 20 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?
Solution
We need the same perimeter as a 60 by 20 rectangle, but the greatest area we can get. right now the perimeter is 160. To get the greatest area while keeping a perimeter of 160, the sides should all be 40. that means an area of 1600. Right now, the area is 20 times 60 which is 1200. 1600-1200=400 which is D.
See Also
| 1999 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
