A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?

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#### Solution

Size of bathroom = 10ft by 8ft

= (10 × 12) inch by (8 × 12) inch

= 120 inch by 96 inch

The largest size of tile required = HCF of 120 and 96

By applying Euclid’s division lemma

120 = 96 × 1 + 24

96 = 24 × 4 + 0

∴ HCF = 24

∴ Largest size of tile required = 24 inches

∴ No. of tiles required =`"Area of bathroom"/"area of 2 tile"`

=`(120xx96)/(24xx24)`

= 5 x 4

= 20 tiles

Concept: Euclid’s Division Lemma

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