Question

a square plot of land has ares equal to that of a rectangular plot having length 218.79 metres and breadth 24.31 metres. Find the perimeter of the square plot​

Answer 1

» Question :

A Square plot of land has area equal to that of a Rectangular plot having length of 218.79 metres and breadth of 24.31 metres. Find the perimeter of the square plot.

» To Find :

The perimeter of the Square plot.

» Given :

• Length of the Rectangular plot = 218.79 m

• Breadth of the Rectangular plot = 24.31 m

» We Know :

For Rectangle :

Area :

$\sf{\underline{\boxed{A_{r} = l \times b}}}$

Perimeter :

$\sf{\underline{\boxed{P_{r} = 2(l + b)}}}$

Where ,

• A = Area of the Rectangle
• P = Perimeter of the Rectangle
• l = length of the Rectangle
• b = Breadth of the Rectangle

For Square :

Area :

$\sf{\underline{\boxed{A_{s} = (a)^{2}}}}$

Perimeter :

$\sf{\underline{\boxed{P_{s} = 4a}}}$

Where ,

• A = Area of the Square
• P = Perimeter of the Square
• a = Equal side of the Square

» Concept :

To find the Perimeter of the Square , first we have to find the side of the Square.

According to the question ,the area of the Rectangle is equal to the Area of the Square .i.e,

$\sf{\therefore A_{r} = A_{s}}$

So , by this we can find the Area of the Square and then by using the formula for finding the area of the Square we can find the side of the Square .

And by the side ,we can find the perimeter of the Square.

» Solution :

Area of the Rectangle :

• Length = 218.79 m
• Breadth = 24.31 m

Formula :

$\sf{\underline{\boxed{A_{r} = l \times b}}}$

By Substituting the value in the formula ,and solving it ,we get :

$\sf{\Rightarrow A_{r} = 218.79 \times 23.31}$

$\sf{\Rightarrow A_{r} = 5318.78 (Approx.) m^{2}}$

Hence ,the area of the Rectangular plot is 5318.78 m².

So ,we get :

$\sf{A_{r} = A_{s} = 5318.78 m^{2}}$

Hence ,the area of the Square is 5318.78 m².

Side of the Square :

• Area of the Square = 5318.78 m²

Formula :

$\sf{\underline{\boxed{A_{s} = (a)^{2}}}}$

By Substituting the value in the formula ,and solving it ,we get :

$\sf{\Rightarrow 5318.79 = (a)^{2}}$

$\sf{\Rightarrow \sqrt{5318.79} = a}$

$\sf{\Rightarrow \sqrt{5318.79} = a}$

$\sf{\Rightarrow 72.93 m = a}$

Hence the side of the Square is 72.93 m

Perimeter of the Square :

• Side = 72.9 m

Formula :

$\sf{\underline{\boxed{P_{s} = 4a}}}$

By Substituting the value in the formula ,and solving it ,we get :

$\sf{\Rightarrow P_{s} = 4 \times 72.93}$

$\sf{\Rightarrow P_{s} = 291.72}$

Hence ,the Perimeter of the Square is 291.72 m

Additional information :

• Surface area of a Cuboid = 2(lb + lh + bh)

• Surface area of a cube = 6(a)²

• Lateral surface area of a Cuboid = 2(l + b)h

• Lateral surface area of a cube = 4(a)².

Answer 2

Given :

• length of the rectangular plot = 218.79 m
• breadth of the rectangular plot = 24.31 m

To find :

• perimeter of square plot

Formulas to be used :

Area of a rectangle ,

$\star \mathtt{A_r = l × b }$

here,

• l = length
• b = breadth

Area of square ,

$\star \mathtt{A_s= a²}$

Perimeter of square ,

$\star \mathtt{P_s= 4 a}$

here ,

• a =side of the square

Solution :

First we need to find the area of the rectangle as the length and breadth of rectangle are already given

Area of rectangle is given by ,

$\star \mathtt{A_r = l × b }$

$\rightarrow\mathtt{A_r = 218.79×24.31 }$

$\rightarrow\mathtt{ \red{A_r =5318.78 \: m}}$

As per the given question ,

$\star\mathtt{A_r = A_ s}$

$\rightarrow\mathtt{A_r = A_ s = 5318.78m}$

_____________________________________

Area of the square = 5318.78 m²....(1)

But area of the square = a ² .....(2)

Equating both the equation we get,

$\rightarrow\mathtt{a²=5318.78}$

$\rightarrow\mathtt{a= \sqrt{5318.78} }$

$\rightarrow\mathtt{ \red{a= 72.92m }}$

____________________________________

Now that we have the side of the square (a)

Let's find it's perimeter

Perimeter of the square ,

$\star \mathtt{P_s= 4 a}$

$\rightarrow\mathtt{P_s= 4 \times 72.92}$

$\rightarrow\mathtt{ \red{P_s=291.68m}}$

Perimeter of the square is 281.68 m

Hope this helps :D