Question

The perimeter of a rectangle is 13 cm and it's width is 11/4cm.find it's area?

Answer 1

Given:

• The perimeter of a rectangle is 13 cm.

• The width of a rectangle ( b ) is 11/4 cm

To find out:

Find the area of rectangle.

Formula used:

• Perimeter of rectangle = 2( l + b )

• Area of rectangle = Length × Breadth

Solution:

Let the length of the rectangle be x

✪ According to question:-

Perimeter of rectangle = 2( l + b )

→ 13 = 2 ( x + 11/4 )

→ 13 = 2x + 2 × 11/4

→ 13 = 2x + 11/2

→ 2x = 13 - 11/2

→ 2x = 26 - 11/2

→ 2x = 15/2

→ x = 15/2 × 1/2

→ x = 15/4

⋆ Length of rectangle = x = 15/4

Now,

Area of rectangle = Length × Breadth

= 15/4 × 11/4

= 165/16 cm²

Answer 2

↪Question :-

• The perimeter of a rectangle is 13 cm and it's width is $\sf{\dfrac{11}{4}\:cm}$.Find it's area?

↪Solution :-

Given :

• Perimeter of the rectangle = 13 cm
• Breadth of the rectangle =$\sf {\dfrac{11}{4}\:cm}$

To Find :

• The area of the rectangle.

Formula used :

$\boxed{\tt{Perimeter\:of\:a\:rectangle= 2(Length + Breadth)}}$

$\boxed{\tt{Area\:of\:a\:rectangle =Length\times Breadth}}$

Now, we are going to find length of the rectangle :

Let the length of the rectangle be x cm.

$\sf{ \implies {Perimeter= 2(Length + Breadth)}} \\ \\ \sf{ \implies {13 = 2(x + \dfrac{11}{4} )}} \\ \\ \sf{ \implies {13 = 2x + \dfrac{11}{2} }} \\ \\ \sf{ \implies {13 - \dfrac{11}{2} }} =2 x \\ \\ \sf{ \implies { \dfrac{26 - 11}{2} }} = 2x \\ \\ \sf{ \implies { \dfrac{15}{2} = 2x}} \\ \\ \sf{ \implies {15 = 4x}} \\ \\ \sf{ \implies { \dfrac{15}{4} = x }} \\ \\ \sf{ \implies {x = \dfrac{15}{4} }}$

$\tt{Thus,\:the \:length\: of\: the\: rectangle\:is\:\dfrac{15}{4} \:cm.}$

Now, we are going to find area of the rectangle :

$\sf{ \implies {Area =Length\times Breadth }} \\ \\ \sf{ \implies {Area = \dfrac{15}{4} \: cm \times \dfrac{11}{4} \: cm }} \\ \\ \sf{ \implies {Area = \dfrac{165}{16} \: {cm}^{2} }}$

$\bf {\therefore{The\:area\:of\:the\:rectangle\:is\: \dfrac{165}{16} \: {cm}^{2}.}}$

$\rule {307}{2}$