Question

If the area of the triangle formed by the points A(a,3), B(5,2) and C(c,3) is 4, then the length of the side AC is ___.

Answer 1

Area of the triangle = 4

$\Rightarrow \frac{1}{2}\left[a\right(2-3)+5(3-3)+c(3-2\left)\right]=4$
$\Rightarrow \left[a\right(2-3)+5(3-3)+c(3-2\left)\right]=8$
$\Rightarrow c-a=8$

Length of AC $=\sqrt{(c-a{)}^2+(3-3{)}^2}$
$\Rightarrow (c-a)=8units$