Question

The area of a square field is 5184 ml. 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

$\sf\small\underline\red{Let:-}$

$\tt{\implies breadth\:_{(rectangle)}=x}$

$\tt{\implies length\:_{(rectangle)}=2x}$

$\sf\small\underline\red{Given:-}$

$\tt{\implies Area\:_{(square\: field)}=5184\:m^2}$

$\tt{\implies length\:_{(rectangle)}=2\times\:of\: breadth}$

$\sf\small\underline\red{To\: Find:-}$

$\tt{\implies Area\:_{(rectangular\: field)}=?}$

$\sf\small\underline\red{Solution:-}$

To calculate the area of rectangular field at first we have find out it's dimensions with the of given clue in the Que. As given in the question perimeter of square field is equal to the perimeter of rectangular field so, here at first we have to find perimeter of square then calculate the dimensions of rectangular field and it's area.

$\sf\small\underline\red{Formula\: Used:-}$

$\tt{\implies Area\:of\: square=side^2}$

$\tt{\implies side^2=5184}$

$\tt{\implies side=\sqrt{5184}}$

$\tt{\implies side=72m}$

• Now calculate perimeter of rectangle:-]

$\tt{\implies Perimeter\:_{(rectangle)}=Perimeter\:_{(square)}}$

$\tt{\implies Perimeter\:_{(rectangle)}=4\times\:side\:_{(square)}}$

$\tt{\implies Perimeter\:_{(rectangle)}=4*72}$

$\tt{\implies Perimeter\:_{(rectangle)}=288m}$

• Now calculate L and B of rectangle:-]

$\tt{\implies 2(l+b)=288}$

$\tt{\implies 2(2x+x)=288}$

$\tt{\implies 2(3x)=288}$

$\tt{\implies 6x=288}$

$\tt{\implies x=48m}$

• Now calculate length and breadth here:-]

$\tt{\implies breadth\:_{(rectangle)}=x=48m}$

$\tt{\implies length\:_{(rectangle)}=2x=2(48)=96m}$

• Now calculate area of rectangle:-]

$\tt{\implies Area\:_{(rectangular\: field)}=length\times\: breadth}$

$\tt{\implies Area\:_{(rectangular\: field)}=96\times\:48}$

$\tt{\implies Area\:_{(rectangular\: field)}=4608m^2}$

$\sf\large{Hence,}$

$\bf{\implies Area\:_{(rectangular\: field)}=4608\:m^2}$

Answer 2

Given :-

Area = 5184 m

Length is twice of breadth

To Find :-

Area

Solution :-

Let the side of square be x

$\sf 5184 = x \times x$

$\sf 5184= x^2$

$\sf \sqrt{5184} = x$

$\sf 72 = x$

Now

Perimeter of square =4s

Perimeter = 4(72)

Perimeter = 288 m

Now

Let length be 2x and breadth be x

288 = 2(2x + x)

288/2 = 2x + x

144 = 3x

144/3 = x

48 = m

Hence

Breadth = 48 m

Length = 2(48) = 96 m

Area = lb.

$\sf Area = 96 \times 48$

$\sf Area = 4608 \; m^2$