Question

Udit runs twice around a square park of side 45m and his brother Sanjay runs only once around a rectangular park of length 34m and breadth 25.5m. How much distance does each boy cover? Who covers more distance and by how much?

Answer 1

Hint:
This problem is related to the perimeter of the figures. When both boys run they run along the edges of the shapes thus we will calculate the perimeters and so the distance covered by Udit and Sanjay.

Complete step by step solution:
Let’s tabulate their run.
Here for both brothers,
distance covered = perimeter of park \[ \times \] number of runs

Distance covered by Udit	Distance covered by Sanjay
Perimeter of square park \[ = 4 \times side \\ \Rightarrow 4 \times 45 \\ \Rightarrow 180m \\ \]	Perimeter of rectangular park\[ = 2\left( {l + b} \right) \\ \Rightarrow 2\left( {34 + 25.5} \right) \\ \Rightarrow 2 \times 59.5 \\ \Rightarrow 119m \\ \]
Distance covered \[ \Rightarrow \] perimeter of park \[ \times \] number of runs\[ \Rightarrow 2 \times 180 \\ \Rightarrow 360m \\ \]	Distance covered \[ \Rightarrow \] perimeter of park \[ \times \] number of runs\[ \Rightarrow 1 \times 119 \\ \Rightarrow 119m \\ \]

Now from table we conclude that Udit covered 360m and Sanjay covered 119m.
Udit covered more distance.
And the distance he covered more than Sanjay is \[360 - 119 = 241m\]

Note:
Most of the students fail to judge whether to find a perimeter or area to solve this type of problem. So let me tell you that in problems like running, fencing a field, bordering with ribbon we find perimeter.
And in this case it is also important to note the number of times he /she ran along the edge of the park.