Solved Examples

Example 1: The Tablecloth Lace

Problem: Akshi wants to put lace all around a rectangular tablecloth that is $3\text{ m}$ long and $2\text{ m}$ wide. Find the length of the lace required.

Solution:

1. Identify the goal: Putting lace “all around” means we need to find the Perimeter.
2. Identify the shape: It is a rectangle.
3. Write the values: Length ($l$) = $3\text{ m}$, Breadth ($b$) = $2\text{ m}$.
4. Apply Formula: $$\begin{aligned} \text{Perimeter} &= 2 \times (l + b) \\ &= 2 \times (3\text{ m} + 2\text{ m}) \\ &= 2 \times (5\text{ m}) \\ &= 10\text{ m} \end{aligned}$$
5. Answer: The length of lace required is 10 m.

Example 2: Running in the Park

Problem: Find the distance travelled by Usha if she takes three rounds of a square park of side $75\text{ m}$.

Solution:

1. Distance of 1 round: This is the perimeter of the square.
2. Formula: Perimeter = $4 \times \text{side}$.
3. Calculate 1 round: $4 \times 75\text{ m} = 300\text{ m}$.
4. Total Distance: She takes 3 rounds. $$\text{Total Distance} = 3 \times 300\text{ m} = 900\text{ m}$$

Example 3: The Uncarpeted Floor

Problem: A floor is $5\text{ m}$ long and $4\text{ m}$ wide. A square carpet of sides $3\text{ m}$ is laid on the floor. Find the area of the floor that is not carpeted.

Solution:

1. Area of Floor (Rectangle): $$A_{floor} = 5\text{ m} \times 4\text{ m} = 20\text{ m}^2$$
2. Area of Carpet (Square): $$A_{carpet} = 3\text{ m} \times 3\text{ m} = 9\text{ m}^2$$
3. Area Not Carpeted: $$\text{Remaining Area} = A_{floor} - A_{carpet} = 20 - 9 = 11\text{ m}^2$$