Question

the perimeter of a rectangle is 72 cm.If the length is double the breadth,determine the area of the rectangle.

Answer 1

D I A G R A M :

$\sf{x \:}\huge\boxed{ \begin{array}{cc} \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{2x}$

• Perimeter = 72 cm

$\Large {\underline { \sf\purple{Clarification :}}}$

Here, we are given that the perimeter of a rectangle is 72 cm and its length is double of its breadth i.e, two times its breadth. We have to find the area of the rectangle.

In order to find the area of the rectangle, we need to find out the dimensions of the rectangle. So, at first we'll form linear equations according to the given question. By solving the equation, we'll find the length and the breadth. After that, we'll substitute the value of length and breadth in the formula of the rectangle to find the area.

$\Large {\underline { \sf \purple{Explication \: of \: steps :}}}$

$\underline{\pmb{ \sf {\maltese \; \; \; Given \: Information \: : \; \; \; }}}$

• Perimeter of rectangle = 72 cm

• Length = Double the breadth.

$\underline{\pmb{ \sf {\maltese \; \; \; To \: calculate \: : \; \; \; }}}$

• Area of the rectangle.

$\underline{\pmb{ \sf {\maltese \; \; \; \: Calculation \: : \; \; \; }}}$

Let,

• Breadth = b

$\underline{ \sf {\maltese \; \; \; According \: to \: the \: question : \; \; \; }}$

$\longrightarrow \sf { Length = 2(Breadth) }$

• Since, length is double the breadth.

$\longrightarrow \sf { Length = 2b}$

$\underline{ \sf \purple {\maltese \; \; \; Finding \: its \: breadth : \; \; \; }}$

We know that,

$\bigstar \: \boxed{\sf { Perimeter_{(Rectangle)} = 2 ( \ell + b) }}$

• $\ell$ = Length
• b = breadth
• Perimeter = 72 cm

$\longrightarrow$ 72 = 2 ( 2b + b )

$\longrightarrow$ 72 = 2 ( 3b )

$\longrightarrow$ 72 = 6b

$\longrightarrow$ $\sf { \dfrac{72}{6} }$ = b

$\longrightarrow$ 12 = b

$\longrightarrow \boxed { \pmb{ \sf \purple { 12 \: cm = Breadth} }}$

$\underline{ \sf \purple {\maltese \; \; \; Finding \: its \: length : \; \; \; }}$

As per the given question,

$\longrightarrow \sf { Length = 2b}$

$\longrightarrow \sf { Length = 2(12) \: cm}$

$\longrightarrow \boxed { \pmb{ \sf \purple { 24 \: cm = Length } }}$

$\underline{ \sf \purple {\maltese \; \; \; Finding \: its \: area : \; \; \; }}$

We know that,

$\bigstar \: \boxed{\sf { Area_{(Rectangle)} = \ell \times b }}$

$\longrightarrow \sf { Area_{(Rectangle)} = (12 \times 24) \: cm^2}$

$\longrightarrow \boxed { \pmb{ \sf \purple { Area_{(Rectangle)} = 288 \: cm^2} }}$

❝ Therefore, area of rectangle is 228 cm². ❞