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Japhet is making small rectangular tiles for a mosaic. Each tile has an area of 7cm^(2) and is 1(1)/(4)cm wide.
How long is each tile?

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cm

Japhet is making small rectangular tiles for a mosaic. Each tile has an area of $7\,\text{cm}^2$ and is $1\frac{1}{4}\,\text{cm}$ wide. $\newline$ How long is each tile? $\newline$ $\square \,\text{cm}$

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Area and perimeter: word problems

Full solution

Q. Japhet is making small rectangular tiles for a mosaic. Each tile has an area of

7\,\text{cm}^2

and is

1\frac{1}{4}\,\text{cm}

wide.

\newline

How long is each tile?

\newline

\square \,\text{cm}

Convert to Improper Fraction: Convert the mixed number for the width of the tile to an improper fraction. $\newline$ $1\frac{1}{4}$ cm = $1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}$ cm
Use Area Formula: Use the area formula for a rectangle, which is $\text{Area} = \text{width} \times \text{length}$ . We know the area ( $7\,\text{cm}^2$ ) and the width ( $\frac{5}{4}\,\text{cm}$ ), so we can solve for the length.
Rearrange for Length: Rearrange the area formula to solve for the length. $Length = \frac{Area}{width}$
Substitute Values: Substitute the known values into the formula. $\newline$ Length = $\frac{7\,\text{cm}^2}{\frac{5}{4}\,\text{cm}}$
Perform Division: Perform the division to find the length. $\newline$ Length = $7\text{cm}^2 \times (\frac{4}{5} \text{cm})^{-1}$ $\newline$ Length = $7\text{cm}^2 \times \frac{4}{5}$ $\newline$ Length = $\frac{28}{5}$ $\newline$ Length = $5.6 \text{cm}$

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