Question

Question 47

The length of a rectangular field is 8 m and breadth is 2 m. If a square field has the same perimeter as this rectangular field, find which field has the greater area.

Answer 1

Given, length of a rectangular field = 8 m

Breadth of rectangular field = 2m

Now, peimeter of rectangle = 2$\times$(Length $\times$)Breadth)

= 2$\times$(8 + 2) = 2$\times$10

= 20 m

$\therefore$ Area of rectangle = Length$\times$Breadth = 8$\times$2 = 16$m^2$

According to the question,

Perimeter of square = Perimeter of rectangle

$\Rightarrow$ 4$\times$Side = 20

$\Rightarrow$ $\frac{4\times Side}{4}=\frac{20}{4}$ [dividing both sides by 4]

$\Rightarrow$ Side = 5 m

Now, area of square = Side$\times$Side = 5$\times$5 = 25 $m^2$

Hence, the area of square field is greater than the area of rectangular field.