the rectangular court yard is 20m 16cm long and 15m 60cm board. it is be provide to be with square shaped tiles of the same side. find the number tiles required to pave the courtyard.
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length of the rectangular Courtyard = 20m 16 cm = 2016 cm
Breadth of the rectangular Courtyard = 15m 60 cm = 1560 cm
HCF(2016, 1560) =?
Prime factorisation of 2016 and 1560 are as follows:
2016 = 2 × 2 ×2 ×2 ×2 ×3 ×3 ×7
1560 = 2 × 2 ×2 ×3 ×5 ×13
→HCF(2016, 1560) = 2 × 2 ×2 ×3 = 24
Least possible number of stones to be paved
= Area of a rectangular courtyard ÷ Area of a square stone
= (2016 × 1560) ÷ (24)2
= 5460
Breadth of the rectangular Courtyard = 15m 60 cm = 1560 cm
HCF(2016, 1560) =?
Prime factorisation of 2016 and 1560 are as follows:
2016 = 2 × 2 ×2 ×2 ×2 ×3 ×3 ×7
1560 = 2 × 2 ×2 ×3 ×5 ×13
→HCF(2016, 1560) = 2 × 2 ×2 ×3 = 24
Least possible number of stones to be paved
= Area of a rectangular courtyard ÷ Area of a square stone
= (2016 × 1560) ÷ (24)2
= 5460
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1
Step-by-step explanation:
Size of the square stone=(H.C.F. of 2016 and 1560) cm=24 cm.
∴ Least number of stones=
Area of courtyard/area of one stone=
2016×1560/24×24=5460
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