Difference between revisions of "2009 AMC 10B Problems/Problem 4"
VelaDabant (talk | contribs) (New page: {{duplicate|2009 AMC 10B #4 and 2009 AMC 12B #4}} == Problem == A rectangular yard contains two flower beds in the shape of congruent i...) |
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| − | <math>\mathrm{(A)}\frac | + | <math>\mathrm{(A)}\frac {1}{8}\qquad |
| − | \mathrm{(B)}\frac | + | \mathrm{(B)}\frac {1}{6}\qquad |
| − | \mathrm{(C)}\frac | + | \mathrm{(C)}\frac {1}{5}\qquad |
| − | \mathrm{(D)}\frac | + | \mathrm{(D)}\frac {1}{4}\qquad |
| − | \mathrm{(E)}\frac | + | \mathrm{(E)}\frac {1}{3}</math> |
== Solution == | == Solution == | ||
Revision as of 10:29, 12 April 2009
- The following problem is from both the 2009 AMC 10B #4 and 2009 AMC 12B #4, so both problems redirect to this page.
Problem
A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths 
and 
meters. What fraction of the yard is occupied by the flower beds?
![[asy] unitsize(2mm); defaultpen(linewidth(.8pt)); fill((0,0)--(0,5)--(5,5)--cycle,gray); fill((25,0)--(25,5)--(20,5)--cycle,gray); draw((0,0)--(0,5)--(25,5)--(25,0)--cycle); draw((0,0)--(5,5)); draw((20,5)--(25,0)); [/asy]](http://latex.artofproblemsolving.com/3/e/e/3ee29f78e4a8eecdb8faec4092f2f1c361a869e4.png)
Solution
Each triangle has leg length 
meters and area 
square meters. Thus the flower beds have a total area of 25 square meters. The entire yard has length 25 m and width 5 m, so its area is 125 square meters. The fraction of the yard occupied by the flower beds is 
. The answer is 
.
See also
| 2009 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 AMC 10 Problems and Solutions | ||
| 2009 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 AMC 12 Problems and Solutions | |
