Difference between revisions of "2001 AMC 10 Problems/Problem 15"
Pidigits125 (talk | contribs) (Created page with '== Problem == A street has parallel curbs <math> 40 </math> feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb betwee…') |
Pidigits125 (talk | contribs) (→Solution) |
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Drawing the problem out, we see we get a parallelogram with a height of <math> 40 </math> and a base of <math> 15 </math>, giving an area of <math> 600 </math>. | Drawing the problem out, we see we get a parallelogram with a height of <math> 40 </math> and a base of <math> 15 </math>, giving an area of <math> 600 </math>. | ||
| − | + | [asy] draw((0,0)--(5,0),linewidth(2)); | |
draw((2.5,5)--(7.5,5)); | draw((2.5,5)--(7.5,5)); | ||
draw((0,0)--(2.5,5)); | draw((0,0)--(2.5,5)); | ||
draw((5,0)--(7.5,5)); | draw((5,0)--(7.5,5)); | ||
| − | draw((2.5,5)--(2.5,0),dashed) | + | draw((2.5,5)--(2.5,0),dashed); [/asy] |
If we look at it the other way, we see the distance between the stripes is the height and the base is <math> 50 </math>. The area is obviously still the same, so the distance between the stripes is <math> 600 \div 50 = \boxed{\textbf{(C)}\ 12} </math>. | If we look at it the other way, we see the distance between the stripes is the height and the base is <math> 50 </math>. The area is obviously still the same, so the distance between the stripes is <math> 600 \div 50 = \boxed{\textbf{(C)}\ 12} </math>. | ||
| − | + | [asy] draw((0,0)--(5,0));draw((2.5,5)--(7.5,5));draw((0,0)--(2.5,5));draw((5,0)--(7.5,5),linewidth(2));draw((2,4)--(7,4),dashed) [/asy] | |
Revision as of 16:00, 16 March 2011
Problem
A street has parallel curbs 
feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is 
feet and each stripe is 
feet long. Find the distance, in feet, between the stripes.
Solution
Drawing the problem out, we see we get a parallelogram with a height of and a base of , giving an area of 
.
[asy] draw((0,0)--(5,0),linewidth(2)); draw((2.5,5)--(7.5,5)); draw((0,0)--(2.5,5)); draw((5,0)--(7.5,5)); draw((2.5,5)--(2.5,0),dashed); [/asy]
If we look at it the other way, we see the distance between the stripes is the height and the base is . The area is obviously still the same, so the distance between the stripes is 
.
[asy] draw((0,0)--(5,0));draw((2.5,5)--(7.5,5));draw((0,0)--(2.5,5));draw((5,0)--(7.5,5),linewidth(2));draw((2,4)--(7,4),dashed) [/asy]
