Question 401669
Start with the formula for the area of a triangle:
{{{A = (1/2)b*h}}} and the area is given a 48 sq.cm., so...
{{{(1/2)b*h = 48}}} but b = h+4, so substitute for b...
{{{(1/2)(h+4)*h = 48}}} Multiply both sides by 2.
{{{(h+4)*h = 96}}} which becomes...
{{{h^2+4h-96 = 0}}} So there's the quadratic in h.  Solve by factoring.
{{{(h-8)(h+12) = 0}}}
{{{h = 8}}} or {{{h = -12}}} Discard the negative solution.
The height is 8cm. and the base is h+4 = 12cm.