Question

Point D is the in center of triangle ABC. Write an expression for the length x in terms of the three side lengths AB, AC, BC.

Hint: Use areas of triangles...A=1/2bh

Answer 1

`\underline{\boxed{x = (A_r)/(AC)}}`

Explanation:

`let \: the \: area \: be \to \: A_r \\ since \: the \: base =AC \\ then \: the \: height = AB \\ but \: AB = 2x \\ hence : the \: area \: A_r= (1)/(2) AC(2x) \\ (2x)AC = 2A_r\\ x = (2(A_r))/(2(AC)) \\ \boxed{x = (A_r)/(AC)}`