Question

(Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of \(x + 15\) and width of \(x + 10\) with a rectangle in the bottom right corner labeled bench that has a length of 5 and width of 1. Write an equation to determine the area, \(A\), of the patio that will be painted.)

- a. \(A = x^2 + 25x + 150\)
- b. \(A = x^2 + 25x - 50\)
- c. \(A = x^2 + 25x + 35\)
- d. \(A = x^2 + 25x + 4\)

Answer 1

The equation to determine the area of the painted patio is A = x^2 + 25x + 145.

Step-by-step explanation:

To determine the area of the patio that will be painted, we need to find the difference between the area of the entire patio and the area of the bench.

The area of the entire patio is given by the product of its length and width, which is (x + 15)(x + 10).

The area of the bench is given by its length multiplied by its width, which is 5 * 1 = 5.

Therefore, the equation to determine the area of the patio that will be painted is:

A = (x + 15)(x + 10) - 5

You can simplify this equation to:

A = x^2 + 25x + 150 - 5

Ultimately, the equation to determine the area of the painted patio is A = x^2 + 25x + 145.