Question

The area of a rectangular room is 45 1/4m². If breadth is 9 3/7m​

Answer 1

Correct Question

The area of a rectangular room is 45 1/4m². If the breadth is 9 3/7 metres. Then, find the perimeter of the room.

Answer

Given :

Area of the room : 45 1/4m²

Breadth of the room : 9 3/7

To find :

The perimeter of the room.

Solution :

To find the perimeter, first we should find the length of the room.

Length of the room :

Let the length of the room be 'l' metres.

$\sf \dashrightarrow {Area}_{(Rectangle)} = Length \times Breadth$

$\sf \dashrightarrow 45 \dfrac{1}{4} = L \times 9 \dfrac{3}{7}$

$\sf \dashrightarrow \dfrac{181}{4} = L \times \dfrac{66}{7}$

$\sf \dashrightarrow L = \dfrac{\dfrac{181}{4}}{\dfrac{66}{7}}$

$\sf \dashrightarrow L = \dfrac{181}{4} \times \dfrac{7}{66}$

$\sf \dashrightarrow L = \dfrac{1167}{264}$

$\sf \dashrightarrow L = \dfrac{289}{88}$

$\sf \dashrightarrow L = 3 \dfrac{25}{88}$

Now, we can find the perimetre of the room.

Perimetre of the room :

$\sf \dashrightarrow {Perimeter}_{(Rectangle)} = 2 \: (Length + Breadth)$

$\sf \dashrightarrow 2 \: \bigg( 3 \dfrac{25}{88} + 9 \dfrac{3}{7} \bigg)$

$\sf \dashrightarrow 2 \: \bigg( \dfrac{289}{88} + {66}{7} \bigg)$

$\sf \dashrightarrow 2 \: \bigg( \dfrac{2023 + 5808}{616} \bigg)$

$\sf \dashrightarrow 2 \: \bigg( \dfrac{7831}{616} \bigg)$

$\sf \dashrightarrow \dfrac{7831}{303} = 25 \dfrac{256}{303}$

Hence, the perimeter of the recatngle is 25 256/303.