Alright, let's solve this step-by-step.
Given:
- The perimeter of the rectangle is 30 cm.
- The length of the rectangle is 8 cm.
Part a: Length + Breadth
The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[ P = 2 \times ( \text{length} + \text{breadth} ) \][/tex]
We know the perimeter [tex]\( P \)[/tex] is 30 cm. Substituting the given perimeter into the formula, we have:
[tex]\[ 30 = 2 \times ( \text{length} + \text{breadth} ) \][/tex]
Now, divide both sides of the equation by 2 to find the sum of the length and the breadth:
[tex]\[ \text{length} + \text{breadth} = \frac{30}{2} \][/tex]
[tex]\[ \text{length} + \text{breadth} = 15 \][/tex]
So the sum of the length and breadth is 15 cm.
Part b: Find the Breadth
We already know the length of the rectangle is 8 cm and we have just found that the length plus breadth is 15 cm.
Thus, we can find the breadth by subtracting the length from this sum:
[tex]\[ \text{breadth} = 15 - \text{length} \][/tex]
[tex]\[ \text{breadth} = 15 - 8 \][/tex]
[tex]\[ \text{breadth} = 7 \][/tex]
Therefore, the breadth of the rectangle is 7 cm.
To summarize:
a) The sum of the length and breadth is 15 cm.
b) The breadth of the rectangle is 7 cm.
