Question 21 (a) - A hall has a length of 9.75 m, breadth of 6.75 m and

Question 21 (a) A hall has a length of 9.75 m, breadth of 6.75 m and height of 5.25 m. What is the length of the longest unmarked ruler that can exactly measure the dimensions of the hall? We need to find Longest unmarked ruler to measure length, breadth & height Since ruler will be smaller than 9.75 m, 6.75 m, 5.25 m We need to find HCF of these 3 numbers Because finding HCF of decimal numbers will be a problem We convert all 3 measurements into cm Thus, Length of room = 9.75 m = 9.75 × 100 cm = 975 cm Breadth of room = 6.75 m = 6.75 × 100 cm = 675 cm Height of room = 5.25 m = 5.25 × 100 cm = 525 cm Therefore, Longest measuring ruler = HCF of 975, 675, 525 HCF of 975, 675, 525 Therefore 450 = 2 × 3 × 3 × 5 × 5 675 = 3 × 3 × 3 × 5 × 5 825 = 3 × 5 × 5 × 11 975 3 5 5 13 325 65 13 1 675 3 3 3 5 225 75 25 5 5 1 525 3 5 5 175 35 7 7 1 Therefore 975 = 3 × 5 × 5 × 13 675 = 3 × 3 × 3 × 5 × 5 525 = 3 × 5 × 5 × 7 Thus, HCF = 3 × 5 × 5 = 75 Thus, Longest Measuring Ruler = 75 cm But since units are in m in question, we need answer in m Longest Measuring Ruler = 75 cm = (75)/(100) = 0.75 m = 3 × 5 × 5 × 3 × 2 = 3 × 5 × 5 × 3 × 3 = 3 × 5 × 5 × 11

Question 21 (a) - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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