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The area of a rectangular shelf is $40$ square inches. The shelf is $4$ inches deep. How wide is it? $\newline$ $\newline$ $\_\_\_\_$ inches

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Area and perimeter: word problems

Full solution

Q. The area of a rectangular shelf is

40

square inches. The shelf is

4

inches deep. How wide is it?

\newline

\newline

\_\_\_\_

inches

Define Width: Let $w$ be the width of the rectangular shelf. $\newline$ To find the area of a rectangle, we use the formula $\text{Area} = \text{width} \times \text{depth}$ .
Calculate Area: Area of the rectangular shelf: $40$ square inches $\newline$ Depth of the shelf: $4$ inches $\newline$ Substitute $40$ for Area and $4$ for depth in the formula $\text{Area} = \text{width} \times \text{depth}$ . $\newline$ $40 = w \times 4$
Substitute Values: Solve for $w$ . $\newline$ $40 = w \times 4$ $\newline$ Divide both sides by $4$ to isolate $w$ . $\newline$ $\frac{40}{4} = \frac{(w \times 4)}{4}$ $\newline$ $10 = w$ $\newline$ Width of the rectangular shelf: $10$ inches

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