Question

pls answer quickly . ​

Answer 1

${ \large{ \red{ \underline{ \pmb{ \frak{Given \: that....}}}}}}$

➼ The perimeter of a square and a rectangle are same.

➼ The length and breadth of the rectangle are 10cm and 8cm respectively

${ \large{ \red{ \underline{ \pmb{ \frak{To \: find....}}}}}}$

➼ The perimeter of the rectangle

➼ The area of the square

${ \large{ \red{ \underline{ \pmb{ \frak{ Solution....}}}}}}$

Here,

➱ We are said that the perimeter of the rectangle and a square are equal.

★ as we have been provided with the dimensions of the rectangle let's find its perimeter, to find the side of the square.

★ Then, Let's find the area of the square with the measurement of its side!

${ \large{ \red{ \underline{ \pmb{ \frak{Calculations....}}}}}}$

Now,

↝ Let's find the perimeter of the rectangle

Formula : -

${ \pink { \boxed{ \frak{perimeter_{(rectangle)} = 2(l + b)}} \star}}$

Where,

• ↠L Stands for length
• ↠ B stands for breadth

Here,

• ↠ Length = 10cm
• ↠ Breadth = 8cm

Putting the values,

${ : \implies} \rm \: perimeter _{(rectangle)} = 2(lenght + breadth) \\ \\ \\ { : \implies} \rm \: perimeter _{(rectangle)} = 2(10 + 8)cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: perimeter _{(rectangle)} = 2 \times 18cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: perimeter _{(rectangle)} = 36cm ^{ \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence, The perimeter of the rectangle is 36cm

As we know that,

• ↝ Perimeter of rectangle = Perimeter of square

So,

• Perimeter of the square is 36cm

Now,

↝ Let's find the side of the square.

Formula : -

${ \pink { \boxed{ \frak{perimeter_{(square)} = 4(side)}} \star}}$

Here,

• ↠ Perimeter = 36cm

Putting the values,

${ : \implies} \rm \: perimeter _{(square)} = 4 \times side \\ \\ \\ { : \implies} \rm \: 36 = 4 \times side \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm side = \cancel\frac{36}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: side = 9cm {}^{ \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence the side of the square is 9cm

Now,

↝ Let's find the area of the square

Formula : -

${ \pink { \boxed{ \frak{area_{(square)} = side \times side}} \star}}$

Here,

• ↠ Side of the square is 9cm

Putting the values,

${ : \implies} \rm \: area_{(square)} = { side }^{2} \\ \\ \\ { : \implies} \rm \: area_{(square)} = {9}^{2} \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: area_{(square)} = 18 {cm}^{2}$

• Hence the area of the square is 18cm²

${ \large{ \red{ \underline{ \pmb{ \frak{Therefore....}}}}}}$

↠The area of the square is 18cm² respectively

${ \large{ \red{ \underline{ \pmb{ \frak{Diagrams....}}}}}}$

❍ Rectangle :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 10 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 8 cm}\end{picture}$

❍ Square :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 9\ cm}\put(4.4,2){\bf\large 9\ cm}\end{picture}$

[Note: Kindly view the diagrams from web]

Answer 2

Step-by-step explanation:

Given:

• Perimeter of the rectangle and perimeter of square is same.
• Length of rectangle = 10cm
• Breadth of rectangle = 8cm

To Find:

• Perimeter of rectangle = ?
• Area of square = ?

Solution:

we have:

• Length = 10cm
• Breadth = 8cm

As we know that,

$\sf\large\boxed{P = 2(l + b) }$

where,

• 'l' is Length.
• 'b' is Breadth.
• 'P' is Perimeter.

Now,putting the values

$\: \sf \rightarrow \: p = 2(10 + 8)cm \\ \\ \: \sf \rightarrow \: p = 2 \times 18cm \\ \\ \: \sf \rightarrow \: p = 36cm$

Hence,Perimeter of rectangle is 36cm.

According to the question,

Perimeter of rectangle = Perimeter of square

So,

• Perimeter of square is 36cm.

We are said to find area so for finding area of square firstly we have to find side of the square.

As we know that,

$\sf\large{side = {\dfrac{P}{4}}}$

where,

• 'P' is Perimeter .

Now put the values

$\: \: \sf \rightarrow \: side = \cancel\frac{36}{4} \\ \\ \: \: \sf \rightarrow \: side = 9 \: cm$

Hence, side of the square is 9cm.

After finding side of the square now we will find area of the square.

$\large\sf\boxed{Area\:of\:square= side × side}$

Now put the values

$\: \: \sf \rightarrow \: area \: = 9 \: cm \: \times 9 \: cm \\ \\ \: \: \sf \rightarrow \: area = 81 {cm}^{2}$

Therefore,area of square is 81$\sf{cm}^{2}$