Question 10 - End-of-Chapter Exercises - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

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Question 10 Two rectangles have the same area and the same perimeter. Does this mean that they are congruent to each other? Let’s look at it step-by-step Step 1 of 6 What does 'Congruent' mean? In geometry, two shapes are congruent if they have the exact same size and shape. You can slide, reflect, or rotate one to fit perfectly on top of the other. Look at the animation: Shape B is congruent to Shape A because it can be moved to perfectly overlap it!tep 2 of 6 The Algebraic Setup Imagine Rectangle 1 has length and width , and Rectangle 2 has length and width . We know they have the exact same area and perimeter. Let's see what this means mathematically. Step 3 of 6 Condition 1: Same Perimeter Perimeter is Length + Width . Since the perimeters are the same, the sum of their length and width must be exactly the same:Step 4 of 6 Condition 2: Same Area Area is Length × Width. Since the areas are the same, the product of their length and width must be exactly the same: Step 5 of 6 The Number Pair Rule In mathematics, if you have two numbers and you know their exact sum and their exact product, there is only ONE possible pair of numbers that can exist. For example, if two numbers add to 7 and multiply to 12 , those numbers MUST be 3 and 4 .Step 6 of 6 The Verdict Therefore, both rectangles must share the exact same dimensions. Even if Rectangle 2 is rotated (Length becomes Width), the physical measurements are identical, meaning they are perfectly congruent.