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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