2013 AMC 10A Problem 3

Below is the professionally curated solution for Problem 3 of the 2013 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 10A solutions, or check the answer key.

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Concepts:triangle area

Difficulty rating: 770

Square $ABCD$ has side length $10.$ Point $E$ is on $\overline{BC},$ and the area of $\triangle ABE$ is $40.$ What is $BE?$

$4$

$5$

$6$

$7$

$8$

Solution:

We have by the formula for the area of a triangle that $40 = \dfrac{1}{2} \cdot 10 \cdot BE.$ This gives us $40 = 5BE$ $BE = 8.$ Thus, E is the correct answer.

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