Area of a sail. The area in square meters for a triangle 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 when area is x^2 +5x+6m^2?

Surely you can find the area of a triangle given the formula. A(5) means area when x is five.

For the second, Area=1/2 base*height. You know ARea (x^2+5x+6), height is x+3, solve for base in terms of x.

To find the area of a sail, we'll use the formula for the area of a triangle: A = (1/2) * base * height.

a) Find A(5):
To find A(5), we'll substitute x = 5 into the formula A(x) = x^2 + 5x + 6:

A(5) = (5)^2 + 5(5) + 6
= 25 + 25 + 6
= 56

Therefore, A(5) = 56 square meters.

b) Find the length of the base when the area is x^2 + 5x + 6m^2:
Given that the height of the sail is x + 3 meters, and the area is x^2 + 5x + 6 square meters, we can rearrange the formula for the area of a triangle to solve for the base:

A = (1/2) * base * height

Substituting the given values, we have:

x^2 + 5x + 6 = (1/2) * base * (x + 3)

Next, we'll solve for the base by isolating it:

2(x^2 + 5x + 6) = base * (x + 3)
2x^2 + 10x + 12 = base * (x + 3)
2x^2 + 10x + 12 = base * x + 3base

Since the length of the base depends on both x and the constant term base, we can write the equation as:

2x^2 + (10 - base) x + 12 = 3base

The length of the base cannot be uniquely determined without knowing the value of the constant term base.