SOLUTION: Area of a sail. The area in square meters for a triangular sail is given by A(x)= x^2+5x+6. a) Find A(5). b) If the height of the sail is x +3 meters, then what is the length o

Question 262615: Area of a sail. The area in square meters for a triangular
sail is given by A(x)= x^2+5x+6.
a) Find A(5).
b) If the height of the sail is x +3 meters, then what is
the length of the base of the sail?

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Area of a sail. The area in square meters for a triangular
sail is given by A(x)= x^2+5x+6.
a) Find A(5).
b) If the height of the sail is x +3 meters, then what is
the length of the base of the sail?

A(5) = 5^2 + 5*5 + 6 so
A(5) = 25 + 25 + 6 = 56
The area of the triangle is 1/2*base*height.
Let B be the base. Then we have
A(x) = x^2 +5x + 6 = 1/2*B*(x+3)
Multiply both sides by 2:
2*(x^2 + 5x + 6) = B*(x+3)
Factor the left side:
2*(x+3)*(x+2) = B*(x+3)
Divide both sides by (x+3)
2*(x+2) = B
B = 2x + 4
If x=5, B = 14
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