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 of t

Question 196365: 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?
Thank you.Angel
Answer by nerdybill(7384) (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).
Simply plug 5 into the equation and solve:
A(5)=5^2 +5(5)+6
A(5)=25 + 25 + 6
A(5)= 56 square meters
.
b) If the height of the sail is x+3 meters, then what is the length of the base of the sail?
Since it is triangular, we know the area is:
(1/2)bh
where
b is base
h is height
.
Area from formula:
x^2 +5x+6
Area from definition of area of a triangle:
(1/2)b(x+3)
.
Set them equal to each other:
x^2 +5x+6 = (1/2)b(x+3)
(x+3)(x+2) = (1/2)b(x+3)
(x+2) = (1/2)b
2(x+2) = b
2x+4 = b
.
So, length of the base of the sail is 2x+4 meters
.
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