Difference between revisions of "2017 AMC 10A Problems/Problem 3"
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Tamara has three rows of two 6-feet by 2-feet flower beds in her garden. The beds are separated and also surrounded by 1-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet? | Tamara has three rows of two 6-feet by 2-feet flower beds in her garden. The beds are separated and also surrounded by 1-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet? | ||
| + | |||
| + | <asy> | ||
| + | draw((0,0)--(0,10)--(15,10)--(15,0)--cycle); | ||
| + | fill((0,0)--(0,10)--(15,10)--(15,0)--cycle, lightgray); | ||
| + | draw((1,1)--(1,3)--(7,3)--(7,1)--cycle); | ||
| + | fill((1,1)--(1,3)--(7,3)--(7,1)--cycle, white); | ||
| + | draw((1,4)--(1,6)--(7,6)--(7,4)--cycle); | ||
| + | fill((1,4)--(1,6)--(7,6)--(7,4)--cycle, white); | ||
| + | draw((1,7)--(1,9)--(7,9)--(7,7)--cycle); | ||
| + | fill((1,7)--(1,9)--(7,9)--(7,7)--cycle, white); | ||
| + | |||
| + | draw((8,1)--(8,3)--(14,3)--(14,1)--cycle); | ||
| + | fill((8,1)--(8,3)--(14,3)--(14,1)--cycle, white); | ||
| + | draw((8,4)--(8,6)--(14,6)--(14,4)--cycle); | ||
| + | fill((8,4)--(8,6)--(14,6)--(14,4)--cycle, white); | ||
| + | draw((8,7)--(8,9)--(14,9)--(14,7)--cycle); | ||
| + | fill((8,7)--(8,9)--(14,9)--(14,7)--cycle, white); | ||
| + | |||
| + | defaultpen(fontsize(8, lineskip=1)); | ||
| + | label("2", (1.2, 2)); | ||
| + | label("6", (4, 1.2)); | ||
| + | defaultpen(linewidth(.2)); | ||
| + | draw((0,8)--(1,8), arrow=Arrows); | ||
| + | draw((7,8)--(8,8), arrow=Arrows); | ||
| + | draw((14,8)--(15,8), arrow=Arrows); | ||
| + | draw((11,0)--(11,1), arrow=Arrows); | ||
| + | draw((11,3)--(11,4), arrow=Arrows); | ||
| + | draw((11,6)--(11,7), arrow=Arrows); | ||
| + | label("1", (.5,7.8)); | ||
| + | label("1", (7.5,7.8)); | ||
| + | label("1", (14.5,7.8)); | ||
| + | label("1", (10.8,.5)); | ||
| + | label("1", (10.8,3.5)); | ||
| + | label("1", (10.8,6.5)); | ||
| + | </asy> | ||
<math>\textbf{(A)}\ 72\qquad\textbf{(B)}\ 78\qquad\textbf{(C)}\ 90\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 150</math> | <math>\textbf{(A)}\ 72\qquad\textbf{(B)}\ 78\qquad\textbf{(C)}\ 90\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 150</math> | ||
Revision as of 17:50, 8 February 2017
Problem
Tamara has three rows of two 6-feet by 2-feet flower beds in her garden. The beds are separated and also surrounded by 1-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet?
![[asy] draw((0,0)--(0,10)--(15,10)--(15,0)--cycle); fill((0,0)--(0,10)--(15,10)--(15,0)--cycle, lightgray); draw((1,1)--(1,3)--(7,3)--(7,1)--cycle); fill((1,1)--(1,3)--(7,3)--(7,1)--cycle, white); draw((1,4)--(1,6)--(7,6)--(7,4)--cycle); fill((1,4)--(1,6)--(7,6)--(7,4)--cycle, white); draw((1,7)--(1,9)--(7,9)--(7,7)--cycle); fill((1,7)--(1,9)--(7,9)--(7,7)--cycle, white); draw((8,1)--(8,3)--(14,3)--(14,1)--cycle); fill((8,1)--(8,3)--(14,3)--(14,1)--cycle, white); draw((8,4)--(8,6)--(14,6)--(14,4)--cycle); fill((8,4)--(8,6)--(14,6)--(14,4)--cycle, white); draw((8,7)--(8,9)--(14,9)--(14,7)--cycle); fill((8,7)--(8,9)--(14,9)--(14,7)--cycle, white); defaultpen(fontsize(8, lineskip=1)); label("2", (1.2, 2)); label("6", (4, 1.2)); defaultpen(linewidth(.2)); draw((0,8)--(1,8), arrow=Arrows); draw((7,8)--(8,8), arrow=Arrows); draw((14,8)--(15,8), arrow=Arrows); draw((11,0)--(11,1), arrow=Arrows); draw((11,3)--(11,4), arrow=Arrows); draw((11,6)--(11,7), arrow=Arrows); label("1", (.5,7.8)); label("1", (7.5,7.8)); label("1", (14.5,7.8)); label("1", (10.8,.5)); label("1", (10.8,3.5)); label("1", (10.8,6.5)); [/asy]](http://latex.artofproblemsolving.com/3/f/3/3f3f120764dbcd2b3383097e2bf5010b26ee5619.png)
See Also
| 2017 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
