Problem 5

{{searchResults.length}} results for “{{searchWords}}” No results found for “{{searchWords}}” × back to contents

§{{x[0]}} {{x[1]}}

Table of Contents

Problem 5: (2012 AMC 10a, 15)

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of $\triangle ABC$?

$\textbf{(A)}\ \frac16 \qquad$ $\textbf{(B)}\ \frac15 \qquad$ $\textbf{(C)}\ \frac29 \qquad$ $\textbf{(D)}\ \frac13 \qquad$ $\textbf{(E)}\ \frac{\sqrt{2}}{4}$

Solution

Exercise 5: Solution

A square of side length $3$ has two unit squares placed side by side along the left part of its top edge, as shown. Segment $AE$ joins the top-left corner of the left unit square to the bottom-right corner of the right unit square. Segment $BD$ joins the top-right corner of the left unit square to the bottom-left corner of the large square. If the segments intersect at $C$, what is the area of $\triangle ABC$?

Search Go to Prev Next

Contact Us