The area of a sheet of paper is $623\dfrac{7}{10}$ sq. cm. If its length is $29\dfrac{7}{10}$cm, find its width.

Given:

Area of a sheet of paper = $623\dfrac{7}{10}\text{ cm}^2 = \dfrac{6237}{10}\text{ cm}^2$

Length = $29\dfrac{7}{10}\text{ cm} = \dfrac{297}{10}\text{ cm}$

Width = ?

The sheet of paper will be in rectangular shape,

∴ Area = Length x Width

Width = Area ÷ Length

Substituting the values in above, we get:

Width = $\dfrac{6237}{10}\text{ cm}^2$ ÷ $\dfrac{297}{10}\text{ cm}$

$\begin{array}{ll} = \Big(\dfrac{6237}{10} \times \dfrac{10}{297}\Big)\text{ cm} & [\text{Reciprocal of } \dfrac{297}{10} \text{ is } \dfrac{10}{297}] \\ = \Big(\dfrac{6237}{1} \times \dfrac{1}{297}\Big)\text{ cm} & \text{[Simplifying 10 and 10 ⇒ Divide by 1]} \\ = \dfrac{6237 \times 1}{1 \times 297} \text{ cm} \\ = \dfrac{6237}{297}\text{ cm} \\ = 21 \text{ cm} \end{array}$

∴ The width of a sheet of paper = 21 cm