Question

m is the perpendicular bisector of ab find the value of x

Answer 1

Given:

m is the bisector of AB

In a triangle ADC,

$DC^2=(6x-25)^2-83^2\ldots\text{ (1)}$

In a triangle BDC

$DC^2=(3x+77)^2-83^2\ldots\text{ (2)}$

From equation(1) and (2),

$\begin{gathered} (6x-25)^2-83^2=(3x+77)^2-83^2 \\ 6x-25=3x+77 \\ 3x=77+25 \\ 3x=102 \\ x=34 \end{gathered}$