Question

The perimeter of a rectangle is 13 cm and its width is 2 3/4 cm. Find its area.
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Answer 1

Given :

Perimetre of rectangle : 13 cm

Width of rectangle : 2¾ cm

To find :

The area of the rectangle.

Solution :

First, we should find the value of length of the rectangle.

Length of the rectangle :

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

$\sf \dashrightarrow 13 = 2 \: \bigg( L + 2 \dfrac{3}{4} \bigg)$

$\sf \dashrightarrow 13 = 2 \: \bigg( L + \dfrac{11}{4} \bigg)$

$\sf \dashrightarrow 13 = 2 \: \bigg( \dfrac{4L + 11}{4} \bigg)$

$\sf \dashrightarrow 13 = \bigg( \dfrac{8L + 22}{4} \bigg)$

$\sf \dashrightarrow \dfrac{8L + 22}{4} = 13$

$\sf \dashrightarrow 8L + 22 = 13 \times 4$

$\sf \dashrightarrow 8L + 22 = 52$

$\sf \dashrightarrow 8L = 52 - 22$

$\sf \dashrightarrow 8L = 30$

$\sf \dashrightarrow L = \dfrac{30}{8}$

$\sf \dashrightarrow L = \dfrac{15}{4}$

$\sf \dashrightarrow L = 3 \dfrac{3}{4}$

Now, we can find the area of the rectangle.

Area of the rectangle :

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

$\sf \dashrightarrow 3 \dfrac{3}{4} \times 2 \dfrac{3}{4}$

$\sf \dashrightarrow \dfrac{15}{4} \times \dfrac{11}{4}$

$\sf \dashrightarrow \dfrac{165}{16} = 10 \dfrac{5}{16}$

Hence the area of the rectangle is 10 5/16 cm.