Q49. - Algebra 1

Question

GEOMETRY Two rectangular walls each with a length of 12 feet and a width of 23 feet need to be painted. It costs \(0.08 per square foot for paint. How much will it cost to paint the walls?

F \)22.08                 H \(34.50

G \)23.04                J $44 .16

Step-by-Step Solution

Answer

It costs $44.16 to paint the walls. The correct option is J.

Step 1. State the formula.

The area of a rectangle is given as $A=lw$, where $A$ is the area, $l$ is the length and $w$ is the width of the rectangle.

Step 2. List the given data.

Two rectangular walls each with a length of 12 feet and a width of 23 feet need to be painted. It costs $0.08 per square foot for paint.

Step 3. Calculate the area.

The length of the wall is 12 feet. So, $l=12$.

 

The width of the wall is 23 feet. So, $w=23$.

 

Put $l=12$ and $w=23$ in $A=lw$ to get,

$$\begin{gathered} A=\left(12\right)\left(23\right) \\ =276 \end{gathered}$$

So, $A=276$

There are two such walls. So, the total area to be painted is $2\times 276=552$

Step 4. Determine the unit.

Since the unit of length and width of the rectangular walls are given as feet, the unit of area must be square feet.

 

So, the total area to be painted is 552 square feet.

Step 5. Evaluate the cost.

The cost of paint is $0.08 per square foot.

 

Then, the cost of paint for 552 square feet is $0.08\times 552=44.16$

 

So, it costs $44.16 to paint the walls.