Question 153016: a triangular sail has an area of x squared +5x+6 squared meters and a height of x+3 meters. find the length of the sail's base.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The problem expects that you know the formula for any triangle is:
area = (1/2)bh
where
b is the length of the base of the triangle
h is the height of the triangle
.
Your problem defines:
area = x^2 + 5x + 6 square meters
h = x+3 meters
.
All we need to do now, is plug in our given values and solve for 'b':
area = (1/2)bh
x^2 + 5x + 6 = (1/2)b(x+3)
Start, by multiplying both sides by 2:
2(x^2 + 5x + 6) = b(x+3)
Now, we divide both sides by (x+3):
[2(x^2 + 5x + 6)]/(x+3) = b
.
At this point, we can factor the numerator:
[2(x^2 + 5x + 6)]/(x+3) = b
[2(x+3)(x+2)]/(x+3) = b
Canceling like-terms we finally get:
2(x+2) = b (this is your answer)
or you could re-write it as:
2x+4 = b
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