SOLUTION: A sail on a particular sailboat has the shape of a triangle with a total area of 52ft squared. The height of the sail is 5 ft greater than the length of "foot" Find the length of

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A sail on a particular sailboat has the shape of a triangle with a total area of 52ft squared. The height of the sail is 5 ft greater than the length of "foot" Find the length of       Log On


   

Question 750582: A sail on a particular sailboat has the shape of a triangle with a total area of 52ft squared. The height of the sail is 5 ft greater than the length of "foot" Find the length of the foot and the height of the sail?

Need help soon please!!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triangle is +A+=+%281%2F2%29%2Ab%2Ah+
Let +h+ = the height of the sail
Let +b+ = the foot of the sail
given:
+A+=+52+ ft2
+h+=+b+%2B+5+ ft
---------------
+A+=+%281%2F2%29%2Ab%2Ah+
+52+=+%281%2F2%29%2Ab%2A%28+b%2B5%29+
+104+=+b%5E2+%2B+5b+
+b%5E2+%2B+5b+-+104+=+0+
I notice that +104+=+13%2A8+, so I can guess that
+b%5E2+%2B+5b+-+104+=+%28+b+%2B+13+%29%2A%28+b+-+8+%29+
++%28+b+%2B+13+%29%2A%28+b+-+8+%29+=+0+
+b+=+8+ ( reject the negative answer )
and, since
+h+=+b+%2B+5+
+h+=+13+
------------
The height is 13 ft and the foot is 8 ft
check:
+A+=+%281%2F2%29%2Ab%2Ah+
+A+=+%281%2F2%29%2A8%2A13+
+A+=+52+
OK