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 plus 20 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 6 and width of 2
Write an equation to determine the area, A, of the patio that will be painted.
A = (x + 20)(x + 10) + 12
A = (x + 20)(x + 10) − 12
A = (x + 26)(x + 12)
A = (x + 14)(x + 8)
A = (x + 20)(x + 10) - 12
Explanation:
The area of the whole rectangular patio is given by multiplying its length and width, which are both (x + 20) and (x + 10) respectively. Therefore, we get:
Area of patio = (x + 20) × (x + 10)
To exclude the area of the bench from the total area of the patio, we need to subtract the area of the bench. The area of the bench is given by multiplying its length and width, which are both 6 and 2 respectively. Therefore, the area of the bench is:
Area of bench = 6 × 2 = 12 square units
So, the equation to determine the area, A, of the patio that will be painted is:
A = (x + 20)(x + 10) - 12
This equation subtracts the area of the bench from the total area of the rectangular patio.
The equation to determine the area, A, of the patio that will be painted is:
A = (x + 20)(x + 10) - (6)(2)
A = (x + 20)(x + 10) - 12