Question 15 of 16intermediate🔧 ApplyShort Answer3 marks

Construct a square whose area is equal to the difference of the areas of squares of sidelengths 5 units and 7 units.

Correct Answer

Step 1: Calculate area of larger square: 7² = 49 sq units

Step 2: Calculate area of smaller square: 5² = 25 sq units

Step 3: Find the difference: 49 - 25 = 24 sq units

Step 4: Find the side length of required square: 24\sqrt{24} = \sqrt{$$4 \times 6$$} = 26\sqrt{6} units

Construction: Form a right triangle with hypotenuse 7 and one leg 5; the other leg will be 24\sqrt{24}, which becomes the side of the required square.

Answer: The required square has side length 24\sqrt{24} = 26\sqrt{6} ≈\approx 4.90 units.

Exercise: Figure it Out (Section 4) | Q: 7 | (Page Page 21)
For More Understanding

Explanation

The chapter demonstrates how Baudhāyana's method can combine squares by using right triangles. For finding the difference of squares, we use the reverse: if we have squares of areas a² and b² (with a > b), then a² - b² = c² where c is the other leg of a right triangle with hypotenuse a and one leg b. Here, 7² - 5² = 49 - 25 = 24, so the required square has side 24\sqrt{24} = 26\sqrt{6}.

Solution Steps

  1. Step 1: Calculate area of larger square: 7² = 49 sq units

  2. Step 2: Calculate area of smaller square: 5² = 25 sq units

  3. Step 3: Find the difference: 49 - 25 = 24 sq units

  4. Step 4: Find the sidelength of required square: 24\sqrt{24} = \sqrt{$$4 \times 6$$} = 26\sqrt{6} units

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