2009 UNCO Math Contest II Problems/Problem 5

Problem

The two large isosceles right triangles are congruent. If the area of the inscribed square $A$ is $225$ square units, what is the area of the inscribed square $B$ ?

$[asy] draw((0,0)--(1,0)--(0,1)--cycle,black); draw((0,0)--(1/2,0)--(1/2,1/2)--(0,1/2)--cycle,black); MP("A",(1/4,1/8),N); draw((2,0)--(3,0)--(2,1)--cycle,black); draw((2+1/3,0)--(2+2/3,1/3)--(2+1/3,2/3)--(2,1/3)--cycle,black); MP("B",(2+1/3,1/8),N); [/asy]$

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2009 UNCO Math Contest II Problems/Problem 5

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