Question

A square and a rectangle have the same perimeter. Calculate the area of the rectangle if the side of the square is 60 cm and the length of the rectangle is 80 cm.​

Answer 1

Answer:

Area of the Rectangle =

$3200 \: {cm}^{2}$

Step-by-step explanation:

Let,

The side of the square, x = 60 cm

The sides of the rectangle are a = 80 cm and b

Parameter of rectangle = Parameter of square

or,

$2(a + b) = 4x$

$2(80 + b) = 4 \times 60$

$b = 40$

The area of the rectangle = ab = 80×40 =

$3200 \: {cm}^{2}$

Answer 2

Given :

• A square and a rectangle have the same perimeter.
• the side of the square is 60 cm and the length of the rectangle is 80 cm.

To Find :

• Calculate the area of the rectangle

Diagrams :

☆ Square :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 60\ cm}\put(4.4,2){\bf\large 60\ cm}\end{picture}$

☆ Rectangle :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 80 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 40 cm}\end{picture}$

Solution:

Now,

• Let's find the perimeter of the square

${ : \implies} \tt \: 60cm \: \times 4 \\ \\ \\ { : \implies} \tt \: 240cm \: \: \: \: \:$

As we know that,

• Perimeter of the square is equal to the perimeter of the rectangle so the perimeter of the rectangle is 240

According to the question,

• The length of the rectangle is 80cm

${ : \implies} \tt \: 2(l + b) = 240cm \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt \: 2(80cm + b) = 240cmm \\ \\ \\ { : \implies} \tt \: 160cm \: + 2b = 240cm \: \: \\ \\ \\ { : \implies} \tt \: 2b = 240 - 160 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt \: 2b = 80cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt \: b = \frac{80}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} { \pink{ \boxed{ \tt{b = 40cm}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So,

• Let's find the area of the rectangle

${ : \implies} \tt area \: = \: l \times b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt area \: = 80cm \times 40cm \\ \\ \\ { : \implies} \tt area \: = { \boxed{ \pmb{ \frak{3200 {m}^{2} }} } \star} \: \: \: \: \:$

• Henceforth the area of the rectangle is 3200m²