Question

The area of a square field is 5184 m?. A 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

Answer:

The area of a square field is 5184 sq. m. A rectangular field, whose length is twice its breadth, has a perimeter equal to the perimeter of the square field. The area of the rectangular field is 4608 sq m.

Step-by-step explanation:

Given: The area of the square field = 5184 sq m.

Find: The area of the rectangular field. ​

If the area of the square field is 5184 sq m

The area of square = $(side)^2$

then, each side of the square field =  $\sqrt{5184}$ = 72 m.

The perimeter of square = 4 (side)

Perimeter of the square field = 4(72) = 288 m.

As per the given condition

The perimeter of rectangle = perimeter of the square

The perimeter of the rectangular field = 288 m.

The length of the rectangular field is 2b, where b = breadth of the field.

Hence 2(2b+b) = 288,

or 3b = 288/2 = 144

or b = 144/3 = 48 m

so length = 2× 48 = 96 m.

Area of the rectangular field = length × breadth

= 96 × 48

= 4608 sq m

So, the area of the rectangular field is 4608 sq m

Answer 2

Answer:

As a result, the rectangular field's area is 4608 square metres.

Step-by-step explanation:

In accordance with the information provided in the question,

Given the data in question the area of a square field is 5184 m

A rectangular field, whose length is twice its breadth, has its perimeter equal to the perimeter of the square field.

We have find the value of  area of the rectangular field. ​

The length of each side of the square field is then 72 metres.

4 is the perimeter of a square (side)

4(72) = 288 m is the square field's perimeter.

According to the circumstances,

The perimeter of a rectangle is equal to the perimeter of a square.

The rectangular field's perimeter is 288 metres.

The rectangular field's length is 2b, where b is the field's width.

As a result, 2(2b+b) = 288, or 3b = 288/2 = 144, or b = 144/3 = 48 m, resulting in length = 2 48 = 96 m.

The rectangular field's area is calculated as follows: length x width = 96 x 48 = 4608 square metres.

As a result, the rectangular field's area is 4608 square metres.