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Difference between revisions of "2000 AMC 8 Problems/Problem 16"

(Created page with "The length of the rectangle is 1000/25=40 meters. The perimeter equals 1000/10=100 meters. Perimeter is 2L+2W. Solving for W, we get 10 inches. The area is 40*10=400 square meter...")
 
(Added problem, Latex'ed solution, added 'see also' box)
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The length of the rectangle is 1000/25=40 meters. The perimeter equals 1000/10=100 meters. Perimeter is 2L+2W. Solving for W, we get 10 inches. The area is 40*10=400 square meters or C.
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==Problem==
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In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?
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<math>\text{(A)}\ 40 \qquad \text{(B)}\ 200 \qquad \text{(C)}\ 400 \qquad \text{(D)}\ 500 \qquad \text{(E)}\ 1000</math>
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==Solution==
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The length <math>L</math> of the rectangle is <math>\frac{1000}{25}=40</math> meters. The perimeter <math>P</math> is <math>\frac{1000}{10}=100</math> meters. Since <math>P_{rect} = 2L + 2W</math>, we plug values in to get:
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<math>100 = 2\cdot 40 + 2W</math>
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<math>100 = 80 + 2W</math>
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<math>2W = 20</math>
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<math>W = 10</math> meters
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Since <math>A_{rect} = LW</math>, the area is <math>40\cdot 10=400</math> square meters or <math>\boxed{C}</math>.
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==See Also==
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{{AMC8 box|year=2000|num-b=15|num-a=17}}

Revision as of 19:34, 30 July 2011

Problem

In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?

$\text{(A)}\ 40 \qquad \text{(B)}\ 200 \qquad \text{(C)}\ 400 \qquad \text{(D)}\ 500 \qquad \text{(E)}\ 1000$

Solution

The length $L$ of the rectangle is $\frac{1000}{25}=40$ meters. The perimeter $P$ is $\frac{1000}{10}=100$ meters. Since $P_{rect} = 2L + 2W$, we plug values in to get:

$100 = 2\cdot 40 + 2W$

$100 = 80 + 2W$

$2W = 20$

$W = 10$ meters

Since $A_{rect} = LW$, the area is $40\cdot 10=400$ square meters or $\boxed{C}$.

See Also

2000 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 15 		Followed by
Problem 17
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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