Question 2 - Think & Reflect (Page 134) - Area of a Triangle - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

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Question 2 - Think & Reflect (Page 134) Think of various rectangles with perimeter 40 units (the sides do not have to be integers). 1. How many such rectangles are there? 2. Among them, is there one whose area is the largest? What are its dimensions? 3. Among all these rectangles, is there one whose area is the smallest? What are its dimensions? Do either of these answers come as a surprise to you? This is one of the most important concepts in geometry: Perimeter does not dictate area. Let’s actually look at various rectangles with perimeter 40 units Now, let’s answer the questions 1. How many such rectangles are there? Because side lengths don't have to be whole numbers. Notice how the slider lets you pick decimals like 18.00. Thus, there are infinite rectangles 2. Is there one whose area is the largest? The area peaks when Length and Width are perfectly equal. Thus, the answer is yes Area of square of 10 × 10 units = 10 × 10 = 100 square units is highest 3. Is there one whose area is the smallest? As you make the length longer and longer (closer to 20), the width gets closer and closer to 0 We can keep getting closer to 0 forever without actually hitting it, so no "minimum" exists. Thus, we can write no smallest rectangle is there