Question

Can someone please help me!!

Answer 1

Answer:

x = 6

Step-by-step explanation:

Use Angle Bisector theorem (look at the picture).

We have the equation:

$\dfrac{3}{x}=\dfrac{x-4}{4}$        cross multiply

$x(x-4)=(3)(4)$          use the distributive property

$x^2-4x=12$           subtract 12 from both sides

$x^2-4x-12=0\\\\x^2+2x-6x-12=0\\\\x(x+2)-6(x+2)=0\\\\(x+2)(x-6)=0\iff x+2=0\ \vee\ x-6=0$

$x+2=0$        subtract 2 from both sides

$x=-2$

$x-6=0$       add 6 to both sides

$x=6$