Questions: Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 22 1/4 cm tall. It has a rectangular shape and an area of 890 cm^2. How wide across is Keala's book cover? cm

Solution Steps

To find the width of Keala's book cover, we can use the formula for the area of a rectangle, which is given by:

\[ \text{Area} = \text{Height} \times \text{Width} \]

We are given the area and the height, so we can rearrange the formula to solve for the width:

\[ \text{Width} = \frac{\text{Area}}{\text{Height}} \]

Given:

• Height = \( 22 \frac{1}{4} \) cm
• Area = 890 cm²

First, convert the mixed number height to an improper fraction or a decimal, then use the formula to find the width.

The height of the book cover is given as \( 22 \frac{1}{4} \) cm. First, we convert this mixed number to a decimal: \[ 22 \frac{1}{4} = 22 + \frac{1}{4} = 22 + 0.25 = 22.25 \text{ cm} \]

The area of the book cover is given as \( 890 \text{ cm}^2 \). We use the formula for the area of a rectangle: \[ \text{Area} = \text{Height} \times \text{Width} \]

Rearrange the formula to solve for the width: \[ \text{Width} = \frac{\text{Area}}{\text{Height}} \] Substitute the given values: \[ \text{Width} = \frac{890}{22.25} \approx 40.0 \text{ cm} \]

Final Answer