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A rectangular courtyard with lenght 10m 50cm and breadth 4m 20cm is to be paved with square stones of the same size the least number of such stones are required are
A. 20
B. 10
C. 8
D. 6
With explaination
Answers
Answer:
Breadth of the courtyard = 10m 44 cm = 1044 cm
Length of the courtyard = 15m 12 cm = 1512 cm
H.C.F of these two measurements will give the side of the square stone
Factors of 1044 = 2*2*3*3*29
Factors of 1512 = 2*2*3*3*3*7
H.C.F = 2*2*3*3*= 36
Side of the square stone = 36cm
Area of the rectangular courtyard = No. of stones * Area of one Stone
Least no. of square stones = 1044*1512 / 36^2 = 1578528/1296 = 1218
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Answer:
10
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.