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? | ||
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− | + | <math>\text{(A)}\ 100 \qquad \text{(B)}\ 200 \qquad \text{(C)}\ 300 \qquad \text{(D)}\ 400 \qquad \text{(E)}\ 500</math> | |
− | + | ==Solution== | |
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− | + | We need the same perimeter as a <math>60</math> by <math>20</math> rectangle, but the greatest area we can get. right now the perimeter is <math>160</math>. To get the greatest area while keeping a perimeter of <math>160</math>, the sides should all be <math>40</math>. that means an area of <math>1600</math>. Right now, the area is <math>20 \times 60</math> which is <math>1200</math>. <math>1600-1200=400</math> which is <math>\boxed{D}</math>. | |
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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}} |
Latest revision as of 13:17, 13 March 2021
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 by rectangle, but the greatest area we can get. right now the perimeter is . To get the greatest area while keeping a perimeter of , the sides should all be . that means an area of . Right now, the area is which is . which is .
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 |
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