Question

The area of a rectangular lawn is the same as the area of a 27m long square garden. If the length of the rectangular lawn is 54 m , find its Perimeter
Please solve the question​

Answer 1

Given

• Area of the rectangular lawn is equal to the area of the square garden.
• Length of each side of the square garden is 27m.
• Length of the rectangular lawn is 54m.

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To find

• Perimeter of the rectangular lawn.

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Solution

• To find the perimeter of the lawn, we should find the breadth of the lawn.

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As it is given in the question that

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★ Area of lawn(rectangle) = Area of garden(square)

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• Formula used

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$\large{\boxed{\boxed{\bf{Area_{(Rectangle)} = l \times b}}}}$

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$\large{\boxed{\boxed{\bf{Area_{(Square)} = (side)^2}}}}$

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• According to the question

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$\tt:\implies\: \: \: \: \: \: \: \: {l \times b = (side)^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {54 \times b = (27)^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {54b = 729}$

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$\tt:\implies\: \: \: \: \: \: \: \: {b = \dfrac{729}{54}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\orange{b = 13.5}}}}$

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• Now, we have b = 13.5m

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Calculating\: perimeter\: of\: the\: lawn}}}$

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$\large{\boxed{\boxed{\bf{Perimeter_{(Rectangle)} = 2(l + b)}}}}$

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• Putting the values

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$\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 2(54 + 13.5)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 2 \times 67.5}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\orange{Perimeter = 135}}}}$

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Hence,

• The perimeter of the rectangular lawn is 135m.

Answer 2

Given

Area of the rectangular lawn is equal to the area of the square garden.

Length of each side of the square garden is 27m.

Length of the rectangular lawn is 54m.

⠀

To find

Perimeter of the rectangular lawn.

⠀

Solution

To find the perimeter of the lawn, we should find the breadth of the lawn.

⠀

As it is given in the question that

⠀

★ Area of lawn(rectangle) = Area of garden(square)

⠀

Formula used

⠀

\large{\boxed{\boxed{\bf{Area_{(Rectangle)} = l \times b}}}}

Area

(Rectangle)

=l×b

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\large{\boxed{\boxed{\bf{Area_{(Square)} = (side)^2}}}}

Area

(Square)

=(side)

2

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According to the question

⠀

\tt:\implies\: \: \: \: \: \: \: \: {l \times b = (side)^2}:⟹l×b=(side)

2

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\tt:\implies\: \: \: \: \: \: \: \: {54 \times b = (27)^2}:⟹54×b=(27)

2

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\tt:\implies\: \: \: \: \: \: \: \: {54b = 729}:⟹54b=729

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\tt:\implies\: \: \: \: \: \: \: \: {b = \dfrac{729}{54}}:⟹b=

54

729

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\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\orange{b = 13.5}}}}:⟹

b=13.5

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Now, we have b = 13.5m

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\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Calculating\: perimeter\: of\: the\: lawn}}}

Calculatingperimeterofthelawn

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\large{\boxed{\boxed{\bf{Perimeter_{(Rectangle)} = 2(l + b)}}}}

Perimeter

(Rectangle)

=2(l+b)

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Putting the values

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\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 2(54 + 13.5)}:⟹Perimeter=2(54+13.5)

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\tt:\implies\: \: \: \: \: \: \: \: {Perimeter = 2 \times 67.5}:⟹Perimeter=2×67.5

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\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\orange{Perimeter = 135}}}}:⟹

Perimeter=135

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Hence,

The perimeter of the rectangular lawn is 135m.