Question

The area of a rectangular field of breadth \[\text{48m}\] is the same as the area of a square field of side \[\text{60m}\]. Find the perimeter of the rectangular field.

Answer 1

Hint: From the given question we are asked to find the perimeter of the rectangular field. For solving this question first we will find the area of the square and then using that area of the square we will find the length of the rectangular field. After finding the rectangular field we will find the perimeter of the rectangular field by adding the length and breadth of the rectangular field.

Complete step-by-step solution:
Firstly as we mentioned in the above we will now find the area of the square. We are given the side of the square as \[\text{60m}\].
The formula for the area of the square is as follows.
\[\Rightarrow \text{area of square}={{s}^{2}}\]
\[\Rightarrow \text{area of square}={{60}^{2}}\]
\[\Rightarrow \text{area of square}=3600\]
We are given that the area of the rectangle is the same as the square. So, we will equate the both areas.
The formula of the area of the rectangle is as follows.
\[\Rightarrow \text{area of rectangle}=l\times b\]
Now we will equate the areas.
\[\Rightarrow l\times b=3600\]
\[\Rightarrow l\times 48=3600\]
Now we will send the constant on the left hand side of the equation to the right hand side of the equation. so, the equation will be reduced as follows.
\[\Rightarrow l=\dfrac{3600}{48}\]
\[\Rightarrow l=75\]
The formulae of the perimeter of the rectangle will be as follows.
\[\Rightarrow perimeter=l+b\]
\[\Rightarrow perimeter=48+75\]
\[\Rightarrow perimeter=123\]

Note: Students must be very careful in doing the calculations. Students should have good knowledge in the concept of areas and perimeters in mathematics to solve this question. We should also know the formulae like,
\[\Rightarrow perimeter=l+b\]
\[\Rightarrow \text{area of rectangle}=l\times b\]
\[\Rightarrow \text{area of square}={{s}^{2}}\]