Question

A school is tiling a wall and needs to choose the tile length.
• The dimensions of the wall are 96 inches and 88 inches.
• All available tiles are squared.
• The side length of a tile can only be in whole inches.



















What is the largest possible side length, in inches, that the school can use?

Answer 1

To find the largest possible side length of the square tiles that can be used for tiling the wall, we need to determine the greatest common divisor (GCD) of the dimensions of the wall.

The dimensions of the wall are:
- Width = 96 inches
- Height = 88 inches

We can find the GCD of 96 and 88 using the Euclidean algorithm.

1. Divide 96 by 88:
\[
96 \div 88 = 1 \quad \text{(quotient)} \quad \text{remainder } = 96 - 88 \cdot 1 = 8
\]

2. Next, we take 88 and divide it by the remainder (8):
\[
88 \div 8 = 11 \quad \text{(quotient)} \quad \text{remainder } = 88 - 8 \cdot 11 = 0
\]

Since the remainder is now 0, the last non-zero remainder (8) is the GCD.

Thus, the largest possible side length of the square tiles that the school can use is:

\[
\boxed{8} \text{ inches}
\]