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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Updated on: 10-Oct-2022

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