Answer:

In a bar diagram, also known as a bar graph, the value represented by a rectangle is proportional to its length. Let's understand why the correct answer is option 'A' by discussing the different components of a bar diagram:

Bar Diagram:
A bar diagram is a visual representation of data using rectangular bars of different lengths. Each bar represents a different category or group, and the length of the bar corresponds to the value it represents. The bars are usually drawn horizontally or vertically, with the length of the bar determined by the data being represented.

Components of a Bar Diagram:
1. Bars: The rectangular bars in a bar diagram represent different values or categories. The length of each bar is determined by the value it represents.
2. Axis: The bar diagram has two axes - the horizontal axis (x-axis) and the vertical axis (y-axis). The axis provides a scale for the values being represented.
3. Labels: The bar diagram also includes labels for the categories or groups being represented. These labels help in identifying and understanding the data.

Understanding the Length of the Bars:
The length of the bars in a bar diagram is directly proportional to the value they represent. This means that as the value increases, the length of the bar also increases. Similarly, as the value decreases, the length of the bar decreases.

Importance of Length in Bar Diagrams:
The length of the bars is the most critical aspect of a bar diagram as it represents the magnitude of the values being depicted. It allows for easy visual comparison between different categories or groups.

Alternative Options:
Let's discuss why the other options are not correct:
- Option 'B' - Width: The width of the bars does not represent the value being depicted. It is typically the same for all bars in a bar diagram.
- Option 'C' - Area: While the area of the bars does represent the magnitude of the values being depicted, the question specifically asks for the value represented by a rectangle. In a bar diagram, the value is directly proportional to the length of the bar, not the area.
- Option 'D' - Perimeter: The perimeter of a rectangle is the sum of all its sides. In a bar diagram, the value being represented does not depend on the perimeter of the rectangle.

Therefore, the correct answer is option 'A' - the value represented by a rectangle in a bar diagram is proportional to its length.