Question 135418
Start with the formula for the area of a triangle:
{{{A = (1/2)bh}}} where: b is the length of the base and h is the length of the height.
In your problem, you have b = h+4 (The base (b) is 4 cm greater than the height (h)) and:
{{{A = 48}}} (The area is 48 sq.cm.), so...
{{{A = (1/2)bh}}} Substitute A = 48, and b = h+4.
{{{48 = (1/2)(h+4)h}}} Simplify and solve for h.
{{{48 = (1/2)(h^2+4h)}}} Multiply both sides by 2.
{{{96 = h^2+4h}}} Subtract 96 from both sdes.
{{{h^2+4h-96 = 0}}} Solve by factoring.
{{{(h+12)(h-8) = 0}}} Apply the zero products rule.
{{{h+12 = 0}}} or {{{h-8 = 0}}}, so...
{{{h = -12}}} or {{{h = 8}}} Discard the negative solution as lengths are positive quantities.
{{{h = 8}}} The height is 8cm.
The base is:
{{{b = h+4}}}
{{{b = 12}}} The base is 12cm.