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Question

# A rectangular room measures 16 feet by 18 feet. The ceiling is 9 feet high. a. Find the total area of the four walls in the room. b. If a gallon of paint costs $37.99 and it covers 400 square feet on average, what is the cost of painting the room, including the ceiling, with two coats of paint? Explain your answer. c. This room is well insulated and is on the north side of the house. How large of an air conditioner would this room require? Round to the next highest thousand BTUs. d. A scale drawing is made of this room using the scale 1 sq$$\mathrm{ft}$=$\frac{1}{4}$ \mathrm{sq}\$ in. What are the dimensions of this room on the drawing?

Solution

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#### a.

Determine the total area of the four walls in the room. Two pairs of walls would have the same measurement.

\begin{align*} &= 2(16 \times 9) + 2(18 \times 9) && \text{Write an expression}\\ &= 2(144) + 2(162) && \text{Multiply the values}\\ &= 288 + 324 && \text{Multiply the values}\\ &= 612 && \text{Add the values} \end{align*}

#### b.

The total area of the four walls is 612 square feet. Determine first the area of the ceiling.

\begin{align*} A &= lw && \text{Write the formula for the area}\\ A &= 16 \times 18 && \text{Substitute the values}\\ A &= 288 && \text{Multiply the values} \end{align*}

Determine the total area that needs to be painted.

$612 + 288 = 900$

Determine the cost of painting the room with two coats of paint.

\begin{align*} &= \dfrac{900}{400} \times 37.99 \times 2 && \text{Write an expression}\\ &= 2.25 \times 37.99 \times 2 && \text{Simplify}\\ &= 170.955 && \text{Multiply the values} \end{align*}

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