Question

For the remaining portion of the living room not covered by the new flooring, Michelle wants to paint the concrete. After carefully measuring the exposed concrete, she determines 6 square feet are already painted and the remaining unpainted area forms a square with side length x. The entire area of concrete, including the painted and unpainted portions, is a total of 31 square feet. Write an equation that could be used to find the unpainted square side length x

Answer 1

To find the equation for the unpainted square side length x, subtract the painted area from the total area. Then, use the formula for the area of a square to set up the equation x^2 = 25. Solve for x by taking the square root of both sides.

Step-by-step explanation:

To find the equation that could be used to find the unpainted square side length x, we first need to calculate the area of the painted portion of the living room. We are given that the total area of concrete, including painted and unpainted portions, is 31 square feet. We are also given that 6 square feet are already painted. Therefore, the area of the unpainted portion is 31 - 6 = 25 square feet.

We know that the remaining unpainted area forms a square with side length x. The area of a square is equal to the side length squared. So, the equation that can be used to find the unpainted square side length x is x^2 = 25.

To solve for x, we can take the square root of both sides of the equation. The square root of x^2 is x, and the square root of 25 is 5. Therefore, the unpainted square side length x is 5 feet.

Answer 2

`x^2 + 6 = 31`

Step-by-step explanation:

Given

`Painted = 6ft^2`

`Total = 31ft^2`

Dimension of unpainted area:

`Length = Width = x` --- Square

Required

Determine an expression to solve for x

First, calculate the area of the unpainted space;

`Area = Length *Width`

`Area = x*x`

`Area = x^2`

The unpainted area, added to the painted area, equals the total area.

So, we have:

`Area + Painted = Total`

`x^2 + 6 = 31`

Hence, the expression is:
`x^2 + 6 = 31`