Question

The area of a rectangular field is $424m^2$ and its breadth is $25m$. Find the length of the rectangle. If this field is exchanged with a rectangular field of the same area and of length $40m$, find:

(a) Breadth of rectangular field

(b) Perimeter of rectangular field

Answer 1

Finding the breadth of the rectangular field

$$\begin{gathered} Areaofrec\tan gle=length\times breadth \\ length=\frac{Areaofrec\tan gle}{breadth} \\ length=\frac{424}{25} \\ length=16.96m \end{gathered}$$

Now, if this field is exchanged with a rectangular field of the same area of length $40m$.

$$\begin{gathered} Areaofrec\tan gle=length\times breadth \\ 424=40\times breadth \\ breadth=\frac{424}{40}=10.6m \end{gathered}$$

Hence, the breadth of the rectangle is $10.6m$.

Now, finding the perimeter of the rectangle.

$$\begin{gathered} Perimterofrec\tan gle=2\left(l+b\right) \\ Perimeterofrec\tan gle=2\left(40+10.6\right) \\ Perimeterofrec\tan gle=101.2m \end{gathered}$$

Hence, the perimeter of rectangle = $101.2m$