MathDB

In triangle

\vartriangle ABC

AB = 5

BC = 7

, and

CA = 8

. Let

E

and

F

be the feet of the altitudes from

B

and

C

, respectively, and let

M

be the midpoint of

BC

. The area of triangle

MEF

can be expressed as

\frac{a \sqrt{b}}{c}

for positive integers

a

b

, and

c

such that the greatest common divisor of

a

and

c

1

and

b

is not divisible by the square of any prime. Compute

a + b + c

Problem Statement