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Difference between revisions of "1998 AJHSME Problems/Problem 13"

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==Problem 13==
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==Problem==
  
 
What is the ratio of the area of the shaded square to the area of the large square?  (The figure is drawn to scale)
 
What is the ratio of the area of the shaded square to the area of the large square?  (The figure is drawn to scale)

Revision as of 11:50, 23 December 2012

Problem

What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale)

[asy] draw((0,0)--(0,4)--(4,4)--(4,0)--cycle); draw((0,0)--(4,4)); draw((0,4)--(3,1)--(3,3)); draw((1,1)--(2,0)--(4,2)); fill((1,1)--(2,0)--(3,1)--(2,2)--cycle,black); [/asy]

$\text{(A)}\ \dfrac{1}{6} \qquad \text{(B)}\ \dfrac{1}{7} \qquad \text{(C)}\ \dfrac{1}{8} \qquad \text{(D)}\ \dfrac{1}{12} \qquad \text{(E)}\ \dfrac{1}{16}$

Solution

We can divide the large square into quarters by diagonals.

Then, in $\frac{1}{4}$ the area of the big square, the little square would have $\frac{1}{2}$ the area.

$\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}=\boxed{C}$


See also

1998 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
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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