Question

the area of a square field is 5184 metre square and rectangular field whose length is twice its breadth has its perimeter equal to the perimeter of the square field find the area of the rectangular field​

Answer 1

area of square field is. 5184m²

side²=5184m²

side=√5184m²

side=72m

perimeter of the rectangle is 2(length+breadth)

breadth=x

length=2x

perimeter of the square=perimeter of the rectangle

4×72m=2(2x+x)

288m=2(3x)

288m=6x

288m÷6=x

48m = x

so, breadth of the rectangle is=48m

length of the rectangle is=2×48m

=96m

so the area of rectangle is length× breadth

= 48m×96m

= 4608m²

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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 ✝

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