Q19. - Algebra 1

Question

A landscape architect is designing a stone path 36 inches wide and 120 inches long. What is the maximum size square stone that can be used so that none of the stones have to be cut?

Step-by-Step Solution

Answer

The maximum size square stone that can be used so that none of the stones have to be cut is 12 inches.

Step 1. Find the factorization of 36 and 120.

Find the factorization of 36 and 120.

$$\begin{gathered} 36=2\cdot 2\cdot 3\cdot 3 \\ 120=2\cdot 2\cdot 2\cdot 3\cdot 5 \end{gathered}$$

Step 2. Find the greatest common factor of 36 and 120.

From the factorization of 36 and 120, it can be noticed that the greatest common factor of 36 and 120 is $2\cdot 2\cdot 3$ or 12.

Therefore, the greatest common factor of 36 and 120 is 12.

Step 3. Determine the maximum size square stone that can be used so that none of the stones have to be cut.

The maximum size square stone that can be used so that none of the stones have to be cut is the greatest common factor of 36 and 120.

Therefore, the maximum size square stone that can be used so that none of the stones have to be cut is 12 inches.