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The area of a square field is $ 576 \mathrm{~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 \( 576 \mathrm{~m}^{2} \), 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 $s$.
Area of the square $=s^2$
$s^2=576$
$s=\sqrt{576}$
$s=24\ m$
Perimeter of the square $=4s$
$=4\times24\ m$
$=96\ m$
Let the breadth of the rectangle be $x$.
This implies,
Length of the rectangle $=2x$
Perimeter of the rectangle $=2(l+b)$
$96=2(x+2x)$
$48=3x$
$x=\frac{48}{3}$
$x=16\ m$
$\Rightarrow 2x=2(16)=32\ m$
Area of the rectangle $=$ Length $\times$ Breadth
$=16\times32$
$=512\ m^2$
The area of the rectangle is $512\ m^2$.
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