Question 373985
Given the base = height + 2 or:
{{{b = h+2}}}
And the area is 12 sq.in.
Start with the formula for the area of a triangle:
{{{A = (1/2)b*h}}} Substitute {{{A = 12}}} and {{{b = h+2}}}
{{{12 = (1/2)(h+2)*h}}} Simplify by multiplying by 2.
{{{2(12) = 2(1/2)(h+2)*h}}} Simplify.
{{{24 = (h+2)*h}}} or
{{{24 = h^2+2h}}} Rearrange into standard quadratic equation form.
{{{h^2+2h-24 = 0}}} Solve by factoring.
{{{(h-4)(h+6) = 0}}} Apply the zero product rule.
{{{h-4 = 0}}} or {{{h+6 = 0}}} which means that...
{{{h = 4}}} or {{{h = -6}}} Discard the negative solution as height (h) is a positive quantity.
{{{h = 4}}}
The height is 4 inches and the base is 6 (h+2)inches.