Question

) The length of a rectangular garden is 36
m and its breadth is 25 m. What is the
perimeter of a square garden whose area
is equal to the area of the rectangular
garden?
​

Answer 1

Correct Question -

The length of a rectangular garden is 36 m and its breadth is 25 m. What is the perimeter of a square garden whose area is equal to the area of the rectangular garden?

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Answer -

Given -

Length of rectangular field = 36 m

Breadth = 25 m

Area of rectangle = Area of square

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To find -

$\implies$Perimeter of square

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Formula used -

Area of rectangle = Length × Breadth

Area of square = side × side

Perimeter of square = 4 × side

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Solution -

Area of rectangle = 36 × 25

$\implies$$\rm{= 900 m^2 }$

Area of rectangle = Area of square

Area of square $\rm{= 900 m^2 }$

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Let the side of square be a

$\implies$$\rm{ a^2 = 900 }$

$\implies$$\rm{ a = 30 }$

Side of square garden = 30 m

Perimeter of square garden = 4 × 30

$\implies$Perimeter of square garden = 120 m

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Thanks

Answer 2

↝To Find :

☞ The perimeter of the square ......

↝Given :

• Length of the rectangle = 36 m
• Breadth of the rectangle = 25 m

↝We Know :

Rectangle :

• Area = Length × Breadth

Square :

• Area = (side)²
• Perimeter = 4 × side

↝Concept :

To find the perimeter of the square , we have to first find the the equal side of the square...

Since it is given that the area of the rectangle is equal to the area of the square , we can use the formula for area of square to find the side of the square ...

Let us determine the side of the square by a variable x...

↝Solution :

Area of the rectangle :

$\boxed{\mathtt{Area = length \times breadth}}$

• lenth = 36 m
• breadth = 25m

Putting the value of Length and breadth in the formula ,we get :

$\mathtt{\Rightarrow Area = 36 \times 25}$

$\mathtt{\Rightarrow Area = 900 m^{2}}$

Hence ,the area of rectangle is 900 m².

ATQ,

Area of rectangle = Area of square

$\therefore$ The area of square is also 900 m².

Side of the square :

• Area = 900 m²

We Know the formula,

$\boxed{\mathtt{Area\:of\:square = (Side)^{2}}}$

Putting the value of area on the formula ,we get :

$\mathtt{\Rightarrow 900 = x^{2}}$

$\mathtt{\Rightarrow \sqrt{900} = x}$

$\mathtt{\Rightarrow 30 m = x}$

Hence , the side of the square is 30 m...

Perimeter of the square :

We know the formula for perimeter of the square :

$\boxed{\mathtt{Perimeter = 4 × side}}$

Putting the value of side , in the formula ,we get :

$\mathtt{\Rightarrow Perimeter = 4 × 30}$

$\mathtt{\Rightarrow Perimeter = 120 m}$

Hence ,the perimeter of the square is 120 m...

↝Extra Information :

• Area of an isosceles triangle : $\dfrac{1}{2}b\sqrt{4a - b}$

where ,

a = side

b = equal sides

• Area of an Equilateral triangle = $\dfrac{\sqrt{3}a^{2}}{4}$

where,

a is the side of the triangle...

• Area of an parallelogram = base × height