Question

3. Area of a square field is 3600m2. A rectangular field whose length is twice its width has
perimeter equal to perimeter of square field. Find the area rectangular field. (3200m)​

Answer 1

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Answer 2

☞︎︎︎ Given :

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★ Area of square field = 3600m²

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★ length of rectangle = 2 × width

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★ peremeter of square = peremeter of rectangle

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☞︎︎︎ To Find :

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★ Area of rectangular field

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❥︎ First we have to find peremeter of square field

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☞︎︎︎ Solution :

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$\: \: \: \: \:$✰ Formula :-

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$\large \boxed{\looparrowright \boxed{\mathtt{area = side \times side}}}$

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➪ 3600m² = side × side

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➪ 3600 = side²

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$\: \: \: \: \:$ ☞︎︎︎ On transposing the terms :

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$\implies \: \mathtt{ \sqrt{3600} = side}$

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$\bigstar \: \large\boxed{ \boxed{ \therefore \: \mathtt{side = 60m}}}$

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☕︎ Now ,

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$\: \: \: \: \:$✰ Formula :-

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$\large \mathtt{ \dashrightarrow \mathtt { \boxed{ \mathtt{perimeter = side \times 4}}}}$

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➪ pereter = 60 × 4

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$\bigstar \: \large\boxed{ \boxed{ \therefore \: \mathtt{perimeter = 240m}}}$

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❥︎ Since,

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✯ perimeter of square = perimeter of rectangle

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➪ 240m = 240m

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✰ Formula :-

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$\mathtt{ \large{\dashrightarrow \mathtt { \boxed{ \mathtt{perimeter = 2(l + b)}}}}}$

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★ since,

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✞︎ length = 2 × width

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➪ 240m = 2 ( 2 × b + b )

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➪ 240 = 4 x 2b

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➪ 240 = 8 b

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$\: \: \: \: \:$☞︎︎︎ On transposing the terms :

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$\implies \mathtt{ \dfrac{240}{8} = breadth}$

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$\bigstar \: \large\boxed{ \boxed{ \: \mathtt{breadth = 40m}}}$

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❥︎ length = 2 × width

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➪ length = 2 × 40m

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$\bigstar \: \large\boxed{ \boxed{ \therefore \mathtt{length = 80m}}}$

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☕︎ Now ,

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$\large { \rightarrow \boxed{\mathtt{area = length \times \: breadth}}}$

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☞︎︎︎ area = 80m × 40m

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$\bigstar \: \large\boxed{ \boxed{ \boxed{ \therefore \mathtt{area= 3200m {}^{2} }}}}$

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