2013 AMC 12A Problem 1

Problem 1 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

The legs of right triangle

ABE

are

AB = 10

and

BE.

From

\tfrac12\cdot 10\cdot BE = 40,

we get

BE = 8.

Thus, the correct answer is E.

Concepts: triangle area · right triangle

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