Problem

2009 AMC 10A Problem 14

Four congruent rectangles are placed as shown. The area of the outer square is 4 times that of the inner square. What is the ratio of the length of the longer side of each rectangle to the length of its shorter side?

[asy] unitsize(6mm); defaultpen(linewidth(.8pt)); path p=(1,1)--(-2,1)--(-2,2)--(1,2); draw(p); draw(rotate(90)*p); draw(rotate(180)*p); draw(rotate(270)*p); [/asy]

\mathrm{(A)}\ 3 \qquad \mathrm{(B)}\ \sqrt {10} \qquad \mathrm{(C)}\ 2 + \sqrt2 \qquad \mathrm{(D)}\ 2\sqrt3 \qquad \mathrm{(E)}\ 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Category: AMC 10A
Points: 3
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