Question

Chen has an unlimited supply of square tiles. She has 1 cm x 1 cm tiles, 2 cm x 2 cm tiles, 3 cm x 3 cm tiles, and so on. Every tile has integer side lengths. A rectangular table top with an 84 cm x 112 cm surface is to be completely covered by identical square tiles, none of which can be cut. Chen wants to use the minimum number of identical tiles to complete the job in order to reduce her costs. Determine the minimum number of identical tiles required to completely cover the table top.

Answer 1

84 = 2 × 2 × 3 × 7
112 = 2 × 2 × 2 × 2 × 7
Highest Common Factor of 84 and 112 = 2 × 2 × 7 = 28

So the tiles should be 28 x 28

84 ÷ 28 = 3
112 ÷ 28 = 4

Total tiles needed = 3 x 4 = 12

Ans: 12 tiles