SOLUTION: A triangular sail has an area of x^2+5x+6 square meters and a height of x+3 meters. Find the length of the sail's base.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A triangular sail has an area of x^2+5x+6 square meters and a height of x+3 meters. Find the length of the sail's base.       Log On


   

Question 154433: A triangular sail has an area of x^2+5x+6 square meters and a height of x+3 meters. Find the length of the sail's base.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the area of any triangle is: Area = (1/2)(Base * Height)


A+=+%281%2F2%29%28b%2Ah%29 Start with the given formula.


x%5E2+%2B+5x+%2B+6+=+%281%2F2%29%28b%29%28x+%2B+3%29 Plug in the given area A=x%5E2+%2B+5x+%2B+6+ and the height h=x%2B3


%28x%5E2+%2B+5x+%2B+6%29%2F%28x+%2B+3%29=+%281%2F2%29%2A%28b%29 Divide both sides by x%2B3


%28%28x%2B3%29%28x%2B2%29%29%2F%28x+%2B+3%29=+%281%2F2%29%2A%28b%29 Factor x%5E2+%2B+5x+%2B+6 to get %28x%2B3%29%28x%2B2%29


%28cross%28%28x%2B3%29%29%28x%2B2%29%29%2Fcross%28%28x%2B3%29%29=+%281%2F2%29%2A%28b%29 Cancel the common terms.


x%2B2=+%281%2F2%29%2A%28b%29 Simplify


2%28x%2B2%29=+b Multiply both sides by 2.


2x%2B4=+b Distribute


So the base is b=2x%2B4