SOLUTION: The base of a triangular sail is 6m shorter than the height.The area is 20 m^2.Find the base and the height of the sail.

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Question 927763: The base of a triangular sail is 6m shorter than the height.The area is 20 m^2.Find the base and the height of the sail.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The base b of a triangular sail is 6m shorter than the height h.
b=h-6m...eq.1
The area is A=20m%5E2....eq.2

A=%281%2F2%29bh...substitute h-6m for b and 20m%5E2 for A

20m%5E2=%281%2F2%29h%28h-6m%29...solve for h
2%2A20m%5E2=h%28h-6m%29
40m%5E2=h%5E2-6m%2Ah
0=h%5E2-6m%2Ah-40m%5E2....use quadratic formula
h+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
h+=+%28-%28-6m%29+%2B-+sqrt%28+%28-6m%29%5E2-4%2A1%2A%28-40m%5E2%29+%29%29%2F%282%2A1%29+
h+=+%286m+%2B-+sqrt%2836m%5E2%2B160m%5E2%29+%29%2F2+
h+=+%286m+%2B-+sqrt%28196m%5E2%29+%29%2F2+

h+=+%286m+%2B-+14m%29+%29%2F2+
h+=+%283m+%2B-+7m%29++
solution:we need only positive solution
h+=+3m+%2B+7m++
highlight%28h+=+10m%29++
find base b

b=h-6m...eq.1
b=10m-6m
highlight%28b=4m%29