MathDB
AMC 8 2003 Problem 25

Source:

July 23, 2011
geometry

Problem Statement

In the figure, the area of square WXYZ is 25cm225 \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 ΔABC\Delta ABC, AB=ACAB = AC, and when ΔABC\Delta ABC is folded over side BC, point A coincides with O, the center of square WXYZ. What is the area of ΔABC\Delta 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("AA", A, NW); label("OO", O, NE); label("BB", B, SW); label("CC", C, NW); label("WW",W , NE); label("XX", X, N); label("YY", Y, N); label("ZZ", Z, SE); [/asy]
<spanclass=latexbold>(A)</span> 154<spanclass=latexbold>(B)</span> 214<spanclass=latexbold>(C)</span> 274<spanclass=latexbold>(D)</span> 212<spanclass=latexbold>(E)</span> 272 <span class='latex-bold'>(A)</span>\ \frac{15}4\qquad<span class='latex-bold'>(B)</span>\ \frac{21}4\qquad<span class='latex-bold'>(C)</span>\ \frac{27}4\qquad<span class='latex-bold'>(D)</span>\ \frac{21}2\qquad<span class='latex-bold'>(E)</span>\ \frac{27}2