SOLUTION: The triangular mainsail on a catamaran has a height 4 feet more than the width of its base. If the area of the sail is 30 square feet, find the height.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The triangular mainsail on a catamaran has a height 4 feet more than the width of its base. If the area of the sail is 30 square feet, find the height.      Log On


   

Question 138788: The triangular mainsail on a catamaran has a height 4 feet more than the width of its base. If the area of the sail is 30 square feet, find the height.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a triangle:
A+=+%281%2F2%29bh 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+=+%281%2F2%29bh Substitute b = h-4
30+=+%281%2F2%29%28h-4%29h Simplify.
30+=+%281%2F2%29%28h%5E2-4h%29 Multiply both sides by 2.
60+=+h%5E2-4h
Subtract 60 from both sides.
h%5E2-4h-60+=+0 Factor.
%28h-10%29%28h%2B6%29+=+0
h-10+=+0 or h%2B6+=+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.