1998 AHSME Problems/Problem 10
Problem 10
A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimter of each of the congruent rectangles is . What is the area of the large square?
![[asy]pathpen = black+linewidth(0.7); D((0,0)--(7,0)--(7,7)--(0,7)--cycle); D((1,0)--(1,6)); D((0,6)--(6,6)); D((1,1)--(7,1)); D((6,7)--(6,1)); [/asy]](http://latex.artofproblemsolving.com/3/5/1/351dd6615f83399259278b9bb833588e02536bc0.png)
Solution
Let the length of the longer side be , and the length of the shorter side be
. We are given that
. However, note that
is also the length of a side of the larger square. Thus the area of the larger square is
.
See Also
1998 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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