Question

The area of a square field is $5184m^2$. Find the area of a rectangular field, whose perimeter is equal to the perimeter of the square field, and whose length is twice is breadth.

Answer 1

Step 1: Finding the side of the square :

Given

area of the square is $5184m^2$

We know that,

Area of square $={\left(side\right)}^2$

So, $5184m^2$$={\left(side\right)}^2$

$\begin{array}{rcl}& \Rightarrow & side=\sqrt{5184}\\ & =& 72m\end{array}$

Thus, the side of the square $=72m$

Step 2: Finding the length and breadth of the rectangle
Let the breadth of the rectangle $=x$

then Length of rectangle $=2x$
Now,

$$\begin{gathered} Perimeterofrec\tan gle=perimeterofsquare \\ \Rightarrow 2(length+breadth)=4\times side \\ \Rightarrow 2(2x+x)=4\times 72 \\ \Rightarrow 2\times 3x=288 \\ \Rightarrow 6x=288 \\ \Rightarrow x=\frac{288}{6}=48m \end{gathered}$$
Thus,

$$\begin{gathered} breadth=x=48m \\ length=2x=96m \end{gathered}$$
Step 3: Finding the area of the rectangle

We know that,

$\begin{array}{rcl}Areaofrec\tan gle& =& length\times breadth\\ & =& 96\times 48\\ & =& 4608m^2\end{array}$

Hence, the area of the rectangle is $4608m^2$