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# igcse problem

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Smith wants to tile a rectangular veranda with dimensions 3.2mx6.4m with a whole number of identical square tiles. His wife wants the tiles to be as large as possible.

a) Find the area of the largest possible tile in cmsquare.

b) How  many tiles will he need to tile the veranda?

Dec 5, 2018

$$\text{veranda }=320 cm\times 640cm\\ \text{we want to find the greatest common factor of }320 \text{ and }640\\ 320=5\times 2^6\\ 640=5 \times 2^7\\ \text{so the LCM of the two is }5\times 2^6 = 320\\ \text{we use square tiles }320cm \times 320cm = 3.2m \times 3.2m\\ \text{we'll need 2 tiles}$$