Question 138788
Start with the formula for the area of a triangle:
{{{A = (1/2)bh}}} where b = the base and h = the height.
You know that:
A = 30 sq.ft.
h = b+4 or b = h-4
Find the height,h.
{{{30 = (1/2)bh}}} Substitute b = h-4
{{{30 = (1/2)(h-4)h}}} Simplify.
{{{30 = (1/2)(h^2-4h)}}} Multiply both sides by 2.
{{{60 = h^2-4h}}}
Subtract 60 from both sides.
{{{h^2-4h-60 = 0}}} Factor.
{{{(h-10)(h+6) = 0}}}
{{{h-10 = 0}}} or {{{h+6 = 0}}}
So, h = 10 or h = -6  Discard the negative solution as the height can only be positive.
The height of the sail is 10 feet.