Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted.

Write an equation to determine the area, [tex]\( A \)[/tex], of the patio that will be painted.

A. [tex]\( A = (x + 20)(x + 11) \)[/tex]
B. [tex]\( A = (x + 15)(x + 10) + 5 \)[/tex]
C. [tex]\( A = (x + 15)(x + 10) - 5 \)[/tex]
D. [tex]\( A = (x + 9)(x + 10) \)[/tex]



Answer :

To determine the area [tex]\( A \)[/tex] of the patio that Marissa will paint, we need to consider the different given equations and find the one that logically fits the scenario where there is a rectangular patio with a bench excluded.

Here are the steps to analyze each given equation:

1. Understanding the given equations:
- [tex]\( A=(x+20)(x+11) \)[/tex]
- [tex]\( A=(x+15)(x+10)+5 \)[/tex]
- [tex]\( A=(x+15)(x+10)-5 \)[/tex]
- [tex]\( A=(x+9)(x+10) \)[/tex]

2. Identifying a typical patio area:
- Typically, the area of a patio can be represented by a product of two dimensions, such as [tex]\( (length \times width) \)[/tex].

3. Considering exclusion of a bench:
- If the bench occupies some specific area, this should be subtracted from the total patio area to get the actual painted area.

4. Analysis of Correct Equation:
- Let's break down each equation logically:

a. Equation [tex]\(A=(x+20)(x+11)\)[/tex]:
- This represents the total area without any exclusion.
b. Equation [tex]\(A=(x+15)(x+10)+5\)[/tex]:
- This represents an area adding an additional fixed part, which doesn't fit our scenario because we are excluding an area.
c. Equation [tex]\(A=(x+15)(x+10)-5\)[/tex]:
- This equation seems promising as it represents the total area minus 5 units, aligning with the idea of excluding a fixed area (the bench).
d. Equation [tex]\(A=(x+9)(x+10)\)[/tex]:
- This is another configuration of the patio dimensions but doesn't account for excluding any area.

5. Identifying the correct option:
- Among these, equation [tex]\( A=(x+15)(x+10)-5 \)[/tex] is the one that fits the scenario of having a bench area subtracted from the total patio area.

Therefore, the correct equation to determine the area [tex]\( A \)[/tex] of the patio that Marissa will paint is:

[tex]\[ A=(x+15)(x+10)-5 \][/tex]

Thus, the corresponding option is:
[tex]\[ \boxed{3} \][/tex]