To find the length of a rectangle when given its perimeter and breadth, let's break the problem down step by step.
We know the following:
- The formula for the perimeter of a rectangle is given by:
[tex]\[ P = 2 \times ( \text{length} + \text{breadth} ) \][/tex]
- The perimeter ([tex]\(P\)[/tex]) of the rectangle is [tex]\(100 \, \text{cm}\)[/tex].
- The breadth ([tex]\(\text{breadth}\)[/tex]) of the rectangle is [tex]\(20 \, \text{cm}\)[/tex].
We need to find the length ([tex]\(\text{length}\)[/tex]).
1. Start with the perimeter formula:
[tex]\[ 100 = 2 \times (\text{length} + 20) \][/tex]
2. First, divide both sides of the equation by 2 to isolate [tex]\(\text{length} + \text{breadth}\)[/tex]:
[tex]\[ 50 = \text{length} + 20 \][/tex]
3. Next, subtract the breadth ([tex]\(20\)[/tex]) from both sides to solve for the length:
[tex]\[ 50 - 20 = \text{length} \][/tex]
4. Simplify the equation:
[tex]\[ 30 = \text{length} \][/tex]
Therefore, the length of the rectangle is [tex]\(30 \, \text{cm}\)[/tex].
