2013 AMC 10A Problem 3

Problem 3 of 25EasierGeometry

Square

ABCD

has side length

10.

Point

E

is on

\overline{BC},

and the area of

\triangle ABE

40.

What is

BE?

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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.

Concepts: triangle area

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.