Certainly! Let's solve this step-by-step.
The perimeter of a table tennis board is given as 9 meters and its breadth is 1.5 meters.
### (i) Finding the Length
To find the length, we can use the formula for the perimeter of a rectangle. The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[ P = 2 \times ( \text{length} + \text{breadth} ) \][/tex]
Given:
- Perimeter ([tex]\( P \)[/tex]) = 9 meters
- Breadth ([tex]\( b \)[/tex]) = 1.5 meters
We need to find the length ([tex]\( l \)[/tex]). Rearranging the perimeter formula to solve for length:
[tex]\[ \text{length} = \frac{P}{2} - b \][/tex]
Now, substitute the given values into the formula:
[tex]\[ \text{length} = \frac{9}{2} - 1.5 \][/tex]
[tex]\[ \text{length} = 4.5 - 1.5 \][/tex]
[tex]\[ \text{length} = 3.0 \][/tex]
So, the length of the table tennis board is 3.0 meters.
### (ii) Finding the Area
To find the area of the rectangle, we use the formula for the area [tex]\( A \)[/tex] of a rectangle:
[tex]\[ A = \text{length} \times \text{breadth} \][/tex]
We have already found the length to be 3.0 meters and the breadth is given as 1.5 meters. Now, substitute these values into the area formula:
[tex]\[ A = 3.0 \times 1.5 \][/tex]
[tex]\[ A = 4.5 \][/tex]
So, the area of the table tennis board is 4.5 square meters.
### Summary
- The length of the table tennis board is 3.0 meters.
- The area of the table tennis board is 4.5 square meters.
