Problem

2003 AMC 8 Problem 25

In the figure, the area of square $WXYZ$ is $25 \text{ cm}^2$ . The four smaller squares have sides $1$ cm long, either parallel to or coinciding with the sides of the large square. In $\triangle ABC$ , $AB = AC$ , and when $\triangle ABC$ is folded over side $\overline{BC}$ , point $A$ coincides with $O$ , the center of square $WXYZ$ . What is the area of $\triangle ABC$ , in square centimeters?

[asy] defaultpen(fontsize(8)); size(225); pair Z=origin, W=(0,10), X=(10,10), Y=(10,0), O=(5,5), B=(-4,8), C=(-4,2), A=(-13,5); draw((-4,0)--Y--X--(-4,10)--cycle); draw((0,-2)--(0,12)--(-2,12)--(-2,8)--B--A--C--(-2,2)--(-2,-2)--cycle); dot(O); label("$A$", A, NW); label("$O$", O, NE); label("$B$", B, SW); label("$C$", C, NW); label("$W$",W , NE); label("$X$", X, N); label("$Y$", Y, S); label("$Z$", Z, SE); [/asy]

$\textbf{(A)}\ \frac{15}4\qquad\textbf{(B)}\ \frac{21}4\qquad\textbf{(C)}\ \frac{27}4\qquad\textbf{(D)}\ \frac{21}2\qquad\textbf{(E)}\ \frac{27}2$

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

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Category: AMC 8
Points: 2
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