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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 221422\frac{1}{4} tall. It has a rectangular shape and an area of 890 cm890\,\text{cm}. How wide across is Keala's book cover?

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Full solution

Q. Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 221422\frac{1}{4} tall. It has a rectangular shape and an area of 890 cm890\,\text{cm}. How wide across is Keala's book cover?
  1. Understand Problem: Understand the problem and identify the given values.\newlineKeala's book cover is a rectangle with a height of 221422 \frac{1}{4} inches tall and an area of 890 cm2890 \, \text{cm}^2. We need to find the width of the book cover.
  2. Convert Height to Decimal: Convert the height of the book cover to a decimal for easier calculation.\newline221422 \frac{1}{4} inches is equal to 22.2522.25 inches.
  3. Identify Formula for Area: Identify the formula for the area of a rectangle.\newlineThe area AA of a rectangle is given by the formula A=l×wA = l \times w.
  4. Rearrange Formula for Width: Rearrange the formula to solve for the width.\newlineTo find the width ww, we use the formula w=Alw = \frac{A}{l}.
  5. Convert Height to Centimeters: Convert the height of the book cover to centimeters.\newlineSince the area is given in cm2cm^2, we need to convert the height from inches to centimeters. There are 2.54 cm2.54\, \text{cm} in an inch, so 22.25 inches×2.54 cm/inch=56.515 cm22.25\, \text{inches} \times 2.54\, \text{cm/inch} = 56.515\, \text{cm}.
  6. Calculate Width Using Area: Calculate the width of the book cover using the area and the converted height. Using the formula w=Alw = \frac{A}{l}, we have w=890 cm256.515 cmw = \frac{890 \, \text{cm}^2}{56.515 \, \text{cm}}.
  7. Perform Division: Perform the division to find the width. \newlinew=890 cm256.515 cm=15.74 cmw = \frac{890 \, \text{cm}^2}{56.515 \, \text{cm}} = 15.74 \, \text{cm} (rounded to two decimal places).

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