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The area of a square field is $5184\ m^2$. 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.
Given:
The area of a square field is $5184\ m^2$. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field.
To do:
We have to find the area of the rectangular field.
Solution:
Let the side of the square be $x$.
Therefore,
$x\times x=5184$
$x^{2}=5184$
$x=\sqrt{5184}$ (Prime factorisation of 5184 is $2 \times 2 \times 2 \times 2 \times 2 \times2\times3 \times 3 \times 3 \times 3$)
$=2 \times 2 \times 2 \times 3 \times 3$
$=72$
The side of the square is $72\ m$.
 Perimeter of the square field $= 72 \times 4\ m$
$= 288\ m$
This implies,
Perimeter of the rectangle $=288\ m$
Let the breadth of the rectangular field be $x$
This implies,
Length of the rectangular field $= 2x$
Perimeter $= 2 (l + b)$
$= 2 (2x + x)$
$= 2\times 3x$
$= 6x$
$6x=288$
$x=\frac{288}{6}$
$x=48\ m$
Length of the rectangular field$= 2x = 2 \times 48$
$= 96\ m$
Breadth $=x = 48\ m$
Area of the rectangular field $= 96 \times 48\ m^2$
$= 4608\ m^2$