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Q.

A rectangular courtyard is 18m 72 cm long and 13m 20 cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

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a

4200

b

4295

c

4290

d

4299

answer is C.

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Detailed Solution

Given that a rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad.

Length of the yard, l = 18 m 72 cm = 1800 cm + 72 cm = 1872 cm Breadth of the yard, b = 13 m 20 cm = 1300 cm + 20 cm = 1320 cm

Length of side of greatest square tile = HCF(1872, 1320)
Euclid's Division Lemma states that if two positive integers a and b exist, then there must be unique values of q and r that satisfy the formula a= bq + r, where 0 ≤ r < b.
Apply Euclid’s division lemma,

1872 = 1320 × 1 + 552 1320 = 552 × 2 + 216 552 = 216 × 2 + 120 216 = 120 × 1 + 96 120 = 96 × 1 + 24 96 = 24 × 4 + 0

∴ HCF 1872, 1320 = 24

∴

Length of side of greatest square tile = 24 cm

Area of rectangular courtyard with length l and breadth b = l × b = 1872 × 1320 cm 2

Area of one square tile

= 24 × 24 cm 2

Question Image

Therefore, least number of tiles of same size required to pave the rectangular courtyard is 4290.
Hence the correct option is 3.

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