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Find the area of isosceles ABC

Source: AIME II 2013, Problem 13

April 4, 2013

geometryratioPythagorean Theoremarea of a triangleHeron's formulaalgebrasystem of equations

Problem Statement

In

\triangle ABC

,

AC = BC

, and point

D

is on

\overline{BC}

so that

CD = 3 \cdot BD

. Let

E

be the midpoint of

\overline{AD}

. Given that

CE = \sqrt{7}

and

BE = 3

, the area of

\triangle ABC

can be expressed in the form

m\sqrt{n}

, where

m

and

n

are positive integers and

n

is not divisible by the square of any prime. Find

m+n

.

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