Question 507537
Start with the formula for the area of a triangle:
{{{A = (1/2)b*h}}} Now substitute A = 18, b = h+5
{{{18 = (1/2)(h+5)*h}}} Multiply both sides by 2.
{{{36 = h^2+5h}}} Rewrite this as:
{{{h^2+5h-36 = 0}}} Solve by factoring.
{{{(h+9)(h-4) = 0}}} Apply the zero product rule.
{{{h+9 = 0}}} or {{{h-4 = 0}}} so...
{{{h = -9}}} or {{{h = 4}}} Discard the negative solution as the height, h, can only be positive.
So the height is 4 cm. and the base 4+5 = 9 cm.