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

2013 AMC 10A Problem 3

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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

Use

AB

as the height of

\triangle ABE

Set

\frac12\cdot AB\cdot BE

equal to the given area

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.