2005 AMC 10A Problems/Problem 8

Problem

In the figure, the length of side $AB$ of square $ABCD$ is $\sqrt{50}$ and $BE$ =1. What is the area of the inner square $EFGH$ ?

[asy] pair D = (0,0); pair C = (1,0); pair B = (1,1); pair A = (0,1); pair H = (0.25,0.6); pair E = foot(C,H,B); pair F = foot(D,C,E); pair G = foot(A,D,F); pair H2 = foot(B,A,G); draw(A--B--C--D--cycle,linewidth(1)); draw(B--H2,linewidth(1)); draw(C--E,linewidth(1)); draw(D--F,linewidth(1)); draw(A--G,linewidth(1)); label(" $A$ ",A,NW);label(" $B$ ",B,NE);label(" $C$ ",C,SE);label(" $D$ ",D,SW); label(" $H$ ",H2,SW);label(" $G$ ",G,SE);label(" $F$ ",F,NE);label(" $E$ ",E,NW);[/asy]

$\textbf{(A)}\ 25\qquad\textbf{(B)}\ 32\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 40\qquad\textbf{(E)}\ 42$

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2005 AMC 10A Problems/Problem 8

Problem