Question

The area of a room is $65\frac{1}{4}{\mathrm{m}}^2.$ If its breadth is $5\frac{7}{16}$ metres, what is its length?

Answer 1

Area of a room = Length $\times$ Breadth
Thus, we have:
$$\begin{gathered} 65\frac{1}{4}=\mathrm{L}\text{ength}\times 5\frac{7}{16} \\ \mathrm{L}\text{ength}=65\frac{1}{4}÷5\frac{7}{16} \end{gathered}$$
$$\begin{gathered} =\left(65+\frac{1}{4}\right)÷\left(5+\frac{7}{16}\right) \\ =\frac{261}{4}÷\frac{87}{16} \\ =\frac{261}{4}\times \frac{16}{87} \\ =\frac{261\times 16}{4\times 87} \\ =\frac{4176}{348} \\ =12\text{m} \end{gathered}$$

Hence, the length of the room is 12 metres.