# Suppose you have a sailboat with one triangular sail. The base of the sail is 4x feet and it's height is 3x + 10 feet. Write a binomial that in terms of x for the area of the sail. Hint: The area of a triangle is 1/2 of the area of a rectangle.

Areabinomial= 1/2(4x)(3x+10)=2x(3x+10)

Binomial....consist of two terms...

22x

## To find the area of the sail, we can use the formula for the area of a triangle which is given by 1/2 * base * height. In this case, the base of the sail is 4x feet and the height is 3x + 10 feet.

So, the area of the sail can be calculated as: Area = 1/2 * (4x) * (3x + 10)

To simplify this expression, we can use the distributive property. We can multiply 1/2 * 4x and 1/2 * (3x + 10) separately.

First, let's multiply 1/2 * 4x. The 2 in the denominator cancels out with the 4, leaving us with 2x.

Next, let's multiply 1/2 * (3x + 10). We can distribute 1/2 to both terms inside the parentheses. This gives us (1/2) * 3x + (1/2) * 10, which simplifies to (3/2)x + 5.

Therefore, the simplified expression for the area of the sail is:

Area = 2x * (3/2)x + 5

Now, let's simplify the binomial 2x * (3/2)x + 5.

Multiplying 2x and (3/2)x gives us (2 * 3)/(2 * 2) * x * x, which simplifies to 6/4 * x^2 or (3/2)x^2.

So, the area of the sail can be expressed as a binomial in terms of x: (3/2)x^2 + 5.

Note: The last expression you mentioned, 22x, does not represent the area of the sail. It appears to be an incorrect calculation.