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.

Answer 1

Answer:

$\underline{\boxed{x = \frac{A_r}{AC}}}$

Step-by-step explanation:

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