Question

The area of a square field is 5184 m². 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.

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Answer 1

Step-by-step explanation:

The area of a square field = 5184m^2

The side of square field =

= side × side = area ( area = 5184m^2)

= area = 2 side

= 5184 = 2side

= 5184 / 2 = side

= side = 2592 ( Is the side of square field)

The perimeter of square field =

= 4×side

= 4× 2592

= 10368 ( ans )

According to the question

perimeter of the square field = perimeter of the rectangular field.

So the perimeter of rectangular field is= 10368m

let the breadth of rectangular field be x.

length = 2x

the perimeter of rectangular field =

= 2 × ( L + B ) = perimeter

= 2× ( 2x + x ) = 10368

= 2 × 3x = 10368

= 3x = 10368/2

= 3x = 5184

= x = 5184 /3

= x = 1728

the breast = x = 1728

the length = 2x

= 2× 1728

=3456

So the length is equal to 1728 and the length is equals to 3456.

Area = length × breadth

= 1728 × 3456

= 5971968 ( ans )

Answer 2

Answer:

4608

Step-by-step explanation:

area of square field = a²

therefore : a² = 5184 m²

so a = √5184=72

according to question

perimeter of square = perimeter of rectangle

4a = 2( l+b )

4*72 = 2 (2x+x) {where x is the breath and 2x is length}

288 = 2(3x)

144=3x

x=48

so breath =48

length = 48*2=96

area of the rectangle field =

length * breadth

48*96 = 4608