Question

The area of a square field is 5184 m. A rectangular field, whose length is twice of its breadth, has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field. re​

Answer 1

Step-by-step explanation:

given,

area of square=5184m

side of square=√5184=72m

then,perimeter of square=72×4=288m

Now,

let breath=x

length=2x

perimeter=2(x+2x)=2×3x=6x

A/Q,

288=6x

or,x=288/6

or,x=48m

so,

l=2×48=96m

b=48

area of rectangular field=48×96=4608m^2

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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