Find the equation of base of Isosceles Traingle Given the two Legs $AB$ and $AC$ of an Isosceles Traingle as $7x-y=3$ and $x-y+3=0$ Respectively. if area of $\Delta ABC$ is $5$ Square units, Find the Equation of the base $BC$
My Try:
The coordinates of $A$ is $(1,4)$. Let the Slope of $BC$ is $m$. Since angle between $AB$ and $BC$ is same as Angle between $AC$ and $BC$ we have
$$\left|\frac{m-7}{1+7m}\right|=\left|\frac{m-1}{1+m}\right|$$ solving which we get $m=2$ or $m=\frac{-1}{2}$
Can any one help me further

You have the vertex $A$ and the equations for the congruent sides.
So you can compute an apex angle $\theta$ with the dot product of two vectors from $A$.
Then, using that angle (or its complement) you can calculate the length of the congruent side $d$ from
$$\frac{d^2 \sin \theta}{2} = 5.$$
This gives you the length to go away from $A$ along the lines, from which you can define the equation for the base.
Note that as given you have four possible equations.
