SOLUTION: sailboat has a triangular sail with an area of 30 square feet. The height of the sail is 7 feet more than the length of the base of thesail. Find the height of the sail?

Algebra ->  Triangles -> SOLUTION: sailboat has a triangular sail with an area of 30 square feet. The height of the sail is 7 feet more than the length of the base of thesail. Find the height of the sail?      Log On


   

Question 451602: sailboat has a triangular sail with an area of 30 square feet. The height of the sail is 7 feet more than the length of the base of thesail. Find the height of the sail?
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
Area, A, of this sail is

A+=+ah%2F2

where a is a base and h is height of the sail.

Since height is 7 feet more than the base it comes to

h+=+a+%2B+7

So area is now

+30+=+a%28a%2B7%29%2F2+ , multiply to get rid of parentheses
+30+=+%28a%5E2+%2B+7a%29%2F2+ , multiply both sides by 2
+60+=+a%5E2+%2B+7a+ , subtract 60 from both sides
+a%5E2+%2B+7a+-+60+=+0+ , this is quadratic equation
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A1%2A%28-60%29+%29%29%2F%282%2A1%29+
We get a=5 or a=-12 and only acceptable solution is a=5 feet.
Height of the seal is
h=a+7
h=5+7
h=12 feet