1987 AJHSME Problems/Problem 12

Problem

What fraction of the large $12$ by $18$ rectangular region is shaded?

$[asy] draw((0,0)--(18,0)--(18,12)--(0,12)--cycle); draw((0,6)--(18,6)); for(int a=6; a<12; ++a) { draw((1.5a,0)--(1.5a,6)); } fill((15,0)--(18,0)--(18,6)--(15,6)--cycle,black); label("0",(0,0),W); label("9",(9,0),S); label("18",(18,0),S); label("6",(0,6),W); label("12",(0,12),W); [/asy]$

$\text{(A)}\ \frac{1}{108} \qquad \text{(B)}\ \frac{1}{18} \qquad \text{(C)}\ \frac{1}{12} \qquad \text{(D)}\ \frac29 \qquad \text{(E)}\ \frac13$

Solution

The shaded region makes up $\frac13$ of the quarter rectangle. The quarter rectangle is then $\frac14$ of the large rectangle, so the shaded region takes up $\frac{1}{3}\times \frac{1}{4}=\frac{1}{12}$ of the large rectangle.

$\boxed{\text{C}}$

1987 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1987 AJHSME Problems/Problem 12

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