The area of a room is $65\dfrac{1}{4}$ sq. metres. If its breadth is $5\dfrac{1}{16}$ metres, what is its length?

We know that area of a rectangle = length × breadth, so length = area ÷ breadth.

Area of the room $= 65\dfrac{1}{4} \text{ sq. m} = \dfrac{261}{4} \text{ sq. m}$

Breadth of the room $= 5\dfrac{1}{16} \text{ m} = \dfrac{81}{16} \text{ m}$

Finding the length,

$\dfrac{261}{4} \div \dfrac{81}{16} = \dfrac{261}{4} \times \dfrac{16}{81} \\[1em] = \dfrac{261 \times 16}{4 \times 81} \\[1em] = \dfrac{4176}{324} = \dfrac{116}{9} \\[1em] = 12\dfrac{8}{9} \text{ m}$

Hence, the length of the room is $\mathbf{12\dfrac{8}{9} \text{ m}}$.