A rectangular courtyard with length 10m 50cm and breadth 4m 20cm is to be paved with square stones of the same size. the least number of such stones required are
Answers
Answer:
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Answer:
Step-by-step explanation:
1 m = 100 cm
10m = 10 * 100 = 1000 cm
4 m = 4 * 100 = 400 cm
Length of the rectangular courtyard = 10m 50 cm = 1000 + 50 = 1050cm
Breadth of the rectangular courtyard = 4m 20 cm = 400 + 20 = 420cm
Area of the rectangular courtyard = Length * Breadth
= 1050 * 420
= 4,41,000 cm²
Prime factorisation of 1050 = 2 * 3 * 5 * 5 * 7
Prime factorisation of 420 = 2 * 2 * 3 * 5 * 7
HCF = 2 * 3 * 5 * 7 = 210
Size of the square stone required to pave the courtyard is 210 cm * 210 cm
Area of the square stone = 210 * 210 = 44,100 cm²
Least possible number of stones to be paved
= Area of a rectangular courtyard ÷ Area of a square stone
= 441000 ÷ 44,100
= 10
∴The least number of square stones of 210 cm * 210 cm that are required to pave the rectangular courtyard are 10.
ANSWERED BY GAUTHMATH