Question

2. A room measures 540cm by 420cm. Find the length of the largest square tiles tha be used to cover the floor without any cutting.

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Answer 1

Area of floor = 420× 540 cm^2

Let the side of a souared tile is ACm.

then, the total area of one tiles = A×A= A^2 cm^2

now,

No of tiles × area of one tiles = area of floor.

No of tiles should be an integer, that means (420 × 540)/ A^2 should be an integer.

write the numerator in terms of its factors:-

420 = 2×2× 3× 5× 7

540 = 2× 2× 3× 3×3× 5

Multiplying both

430× 540 = 4^2 × 9^2 × 5^2 × (7^0.5)^2

Hence largest length = 4× 9×5 × 7^0.5 = 476.335 Cm.

or simply

find the sugare root of product of 420 and 540.

ans = 476.335 cm.