Square ABCD has side length 10. Point E is on BC, and the area of △ ABE is 40. What is BE?

2013 AMC 12A Problem 1

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Square

ABCD

has side length

10.

Point

E

is on

\overline{BC},

and the area of

\triangle ABE

40.

What is

BE?

4

5

6

7

8

The legs of right triangle

ABE

are

AB

and

BE

Set

\tfrac12\cdot AB\cdot BE = 40

with

AB = 10

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.