Question

The area of a square field is 5184 m² . Find the area of a rectangular field, whose perimeter is equal to the perimeter of the square field and whose length is twice of its breadth.​

Answer 1

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• Side of square field= √area
• Side = √5184 = 72
• Perimeter = 4 × side = 4×72
• P = 288m
• Perimeter of rectangle is same as that of square field
• 2(l+b)=288____(1)
• Given L = 2b for rectangle, Replace this value in (1)
• 2(3b)=288
• b= 288 ÷ 6
• B = 48m,L = 2b = 96m
• Area of rectangle = L×B = 48×96
• = 4608m^2

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Answer 2

Given:-

• Area of square field = 5184 m².

To Find:-

• Area of rectangle.

Formula to be used:-

• Perimeter of square = 4a

• Perimeter of rectangle = 2 (l + b)

Solution:-

• Let the side of square field as a.

Then,

• ⇒ a² = 5184 m²
• ⇒ a = √5184 m
• ⇒ a = 2 × 2 × 2 × 9 = 72 m

Now,

• Perimeter of square = 4a
• Perimeter of square = 4(72)
• Perimeter of square = 288 m

Now,

• Perimeter of rectangle = 2 (l + b)

• ⇒ 288 = 2 (l + b)

As length is twice of its breadth,

• ⇒ 288 = 2 × (2b + b)
• ⇒ 288 = 2 × 3b
• ⇒ 288/2 = 3b
• ⇒ 144 = 3b
• ⇒ 144/3 = b
• ⇒ b = 48

Here, breadth is 48 m

Now length,

• Length = 2 × 48 = 96 m

• Now, Area of rectangle  

• Area of rectangle = l × b

• Area of rectangle = 96 × 48

• Area of rectangle = 4608 m².

✝ Hence, the Area of rectangle is 4608 m² ✝