1981 AHSME Problems/Problem 2

Problem

Point $E$ is on side $AB$ of square $ABCD$ . If $EB$ has length one and $EC$ has length two, then the area of the square is

$\textbf{(A)}\ \sqrt{3}\qquad\textbf{(B)}\ \sqrt{5}\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 2\sqrt{3}\qquad\textbf{(E)}\ 5$

Solution

Note that $\triangle BCE$ is a right triangle. Thus, we do Pythagorean theorem to find that side $BC=\sqrt{3}$ . Since this is the side length of the square, the area of $ABCD$ is $\boxed{\textbf{(C)}\ 3}$ .

~superagh

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1981 AHSME Problems/Problem 2

Problem

Solution