Question

Priya walks around a square garden of side 65m. Bhavya walks around a rectangular garden of length 60m and breadth 45m. Who walks more and how much more?

Answer 1

Hint: To solve this question, we will calculate the path they both traveled by using the formula of the perimeter of the square and of the rectangle. The perimeter of the square of side ‘a’ is given by ‘4a’ and the perimeter of the rectangle of length l and breadth b is given by 2(l + b). Finally, we will calculate whose path is more and by how much.

Complete step-by-step solution:
Priya is walking around a square garden and the side measure of the square garden is 65m.

Now the area she walks is calculated by calculating the perimeter of the square. The perimeter of the square of side length ‘a’ is given by 4a (as there are 4 sides of a square). Here, the perimeter of the square garden will be
\[\text{Perimeter of square garden}=4\times 65m\]
65m is the side length of the square.
\[\Rightarrow \text{Perimeter of square garden}=4\times 65\]
\[\Rightarrow \text{Perimeter of square garden}=260m\]
Hence, the area that Priya walks is 260m……….……(i).
Now, we will calculate the path measure which Bhavya walks. Bhavya walks around a rectangular garden of length 60m and breadth 45m.

The perimeter of the rectangle of length ‘l’ and breadth b is given by
\[\text{Perimeter}=2\left( l+b \right)\]
\[\text{length }l=60m\]
\[\text{breadth }b=45m\]
Then the perimeter of the rectangle will be
\[\text{Perimeter of rectangle}=2\left( l+b \right)\]
\[\Rightarrow \text{Perimeter of rectangle}=2\left( 60+45 \right)\]
\[\Rightarrow \text{Perimeter of rectangle}=2\left( 105 \right)\]
\[\Rightarrow \text{Perimeter of rectangle}=210m\]
The perimeter of the rectangle in which Bhavya walks is 210m……(ii)
We can observe from equations (i) and (ii) that Priya walks more. The distance which she walks more is given by
\[\Rightarrow 260-210=50\]
Therefore, 50m more is what Priya walked from Bhavya.

Note: The possibility of a mistake here in this question can be calculating the area of the square and the area of the rectangle to calculate the path they both moved around. Remember that they are walking around the square and rectangle and not all of the gardens. Because, they are walking around, so we only need the perimeter and not the area of the square and rectangle.