RBSE Solutions Class 8 Maths Chapter 12 Linear Graph Exercise 12.2

Question 1. Length of a side of an equilateral triangle and square is x cm. Find their perimeter, draw the graph between length and perimeter. [Hint = Perimeter of ∆ = (x + x + x) cm.]
Answer:
(1) For an equilateral triangle:
The perimeter is calculated as 3 times the length of one side. So, if the side length is \( x \), the perimeter \( P = 3x \).
The relationship between side length (x) and perimeter (P) is shown in the table below.

The graph showing this relationship is provided in the solution.
(2) For a square:
The perimeter is calculated as 4 times the length of one side. So, if the side length is \( x \), the perimeter \( P = 4x \).
The relationship between side length (x) and perimeter (P) for a square is shown in the table below.

The graph for this relationship is also provided in the solution. Understanding these basic perimeter formulas helps in quickly calculating the boundary of many common shapes.
In simple words: For an equilateral triangle, the perimeter is 3 times the side length. For a square, it's 4 times the side length. The tables show the numbers for each. You can then use these numbers to draw graphs, which are shown in the images.

🎯 Exam Tip: When drawing graphs from tables, ensure you label both axes correctly and choose an appropriate scale to fit all data points clearly.

Question 2. Length of a rectangle is double of its breadth. Draw the graph between area and breadth of rectangle. (Hint : Area of rectangle A = 2x x x = 2x²)
Answer: For this rectangle, the length is twice its breadth. If the breadth is \( x \), then the length is \( 2x \). The area of a rectangle \( A \) is found by multiplying its length and breadth. So, the area becomes \( A = \text{Length} \times \text{Breadth} = 2x \times x = 2x^2 \). The table shows how the area changes as the breadth increases, and this data is used to draw the graph. This relationship shows that the area grows much faster than the breadth because it's a squared relationship.

In simple words: The rectangle's length is twice its width. To find the area, you multiply length by width, which gives \( 2x^2 \). The table shows the area for different widths. The graph (shown in the figure) visually displays this.

🎯 Exam Tip: Remember that area calculations involve squared units. When plotting a quadratic relationship like \( y = x^2 \), the graph will be a curve, not a straight line.

Question 3. According to the following table, draw the graph between time and simple interest.
Answer: The table provided shows the simple interest earned over different periods of time. To draw the graph, plot the time (in years) on the x-axis and the simple interest (in Rs) on the y-axis. Then, connect these points to see the linear relationship between time and simple interest. Simple interest calculates earnings only on the original amount, making it a straightforward, linear growth.

In simple words: Use the numbers from the table. Put 'Time' on the bottom line (x-axis) and 'Simple Interest' on the side line (y-axis). Then, draw points and connect them to make a graph.

🎯 Exam Tip: Always check if the relationship is linear (forms a straight line) or non-linear (forms a curve) by observing the data points and the type of equation.

Question 4. Draw a graph representing the relation between time and distance.
Answer: To represent the relationship between time and distance, use the given table to draw a graph. Plot the time values on the horizontal axis (x-axis) and the corresponding distance values on the vertical axis (y-axis). Connecting these points will show how distance changes as time passes. When distance increases steadily with time, it indicates a constant speed.

In simple words: Take the numbers from the table. Put 'Time' on the bottom (x-axis) and 'Distance' on the side (y-axis). Mark the points and draw a line through them to show the graph.

🎯 Exam Tip: The slope of a distance-time graph represents speed. A straight line indicates constant speed, while a curved line suggests changing speed.

Question 5. According to the following table, draw the graph and explain this graph pass through the origin.
Answer: The provided table shows the simple interest earned on different fixed deposit amounts. To draw the graph, plot the fixed deposit amounts on the x-axis and the simple interest on the y-axis. The graph formed by these points is a straight line, and it passes through the origin (0,0). This is because if there is no fixed deposit (0 Rs), there will be no simple interest (0 Rs). A graph passing through the origin shows a direct proportion, meaning if one value is zero, the other is also zero.

In simple words: Use the table to draw a graph with 'Fixed Deposit' on the x-axis and 'Simple Interest' on the y-axis. This graph will be a straight line that starts from the point (0,0). This means if you deposit zero money, you get zero interest.

🎯 Exam Tip: When a graph passes through the origin, it indicates that the two quantities are directly proportional, meaning one quantity is a constant multiple of the other.