Question

thearea
of rectangular room
is 65 1/4 m^2?
If its breadth is 5 7/16 m. What is its length?​

Answer 1

Answer :-

• Length of the Room = 12 m

Given :-

• $\sf Area \: of \: Room \longrightarrow 65 \: \dfrac{1}{4} = \bold{ \dfrac{261}{4} } \: m^2$
• $\sf Width \: of \: Room \longrightarrow 5 \: \dfrac{7}{16} = \bold{ \dfrac{87}{16} } \: m$

To Find :-

• Length of the Room = ?

Explanation :-

As above given, we have Area & Width of the room. So, Let the Length of the Room to be 'x' m.

$\blue { \boxed { \bf \bigstar \: Area \: of \: Room = Length \times Width \: \bigstar}}$

$\sf : \: \longmapsto Length \times Width = Area \: of \: Room$

$\sf : \: \longmapsto x \times \dfrac{87}{16} = \dfrac{261}{4}$

$\sf : \: \longmapsto x =\dfrac{261}{4} \div \dfrac{87}{16}$

$\sf : \: \longmapsto x =\dfrac{261}{4} \times \dfrac{16}{87}$

$\sf : \: \longmapsto x =\dfrac{\cancel{261}}{\cancel{4}} \times \dfrac{\cancel{16}}{\cancel{87}}$

$\sf : \: \longmapsto x = 3 \times 4$

$\green { \underline { \boxed { \sf : \: \longmapsto \bold{x = 12 \: m} \quad \star }}}$

For verification,

$\sf : \: \longmapsto Length \times Width = Area \: of \: Room$

$\sf : \: \longmapsto 12 \times \dfrac{87}{16} = \dfrac{261}{4}$

$\sf : \: \longmapsto \dfrac{1044}{16} = \dfrac{261}{4}$

$\sf : \: \longmapsto 65 \: \dfrac{1}{4} = \dfrac{261}{4}$

$\sf : \: \longmapsto \dfrac{261}{4} = \dfrac{261}{4}$

$\bf : \: \longmapsto L.H.S = R.H.S \quad \star$

Hence, the Length of the room is 12 m.