Question

william is planning to create a rectangular mosaic which measures 120 cm by 144 cm. the mosaic will be covered completely with square pieces of colored glass. william has decided that he will purchase only one size of glass squares, and he does not plan to cut any of the pieces. if the art supply store only sells the glass squares in whole - number side lengths (measured in centimeters), find the smallest number of squares which william could use for his mosaic. a) 1440 b) 288 c) 720 d) 2160 e) 30 f) none of the above your answer is incorrect.

Explanation:

Step1: Find the greatest - common divisor (GCD) of 120 and 144

We use the Euclidean algorithm. First, divide 144 by 120: $144 = 120\times1 + 24$. Then divide 120 by 24: $120=24\times5+0$. So the GCD of 120 and 144 is 24.

Step2: Calculate the number of squares

The area of the rectangular mosaic is $A = 120\times144$ square - centimeters. The area of each square piece is $24\times24$ square - centimeters. The number of squares $n=\frac{120\times144}{24\times24}=\frac{120}{24}\times\frac{144}{24}=5\times6 = 30$.

Answer:

30