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? 


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