Answer:
The largest size tile is 12 inches in length, 144 inches² in areas
Step-by-step explanation:
The question is essentially asking for the highest common factor of 60 and 48;
Both rows are made of the same tiles, meaning tiles that have the same side length, let's say this length is x;
This means a certain number of tiles can be lined up to create a line of tiles 60 inches in length and another number could be lined up to create a line of tiles 48 inches of length;
In other words, x multiplied by some number will give 60 and x multiplied by another number will give 48;
This means x is a factor of both 60 and 48;
And since we are asked for the largest size tile possibly used, we want the highest common factor to both 60 and 48;
To do this, we first identify the prime factors of 60:
60 = 30 × 2
= 15 × 2 × 2
= 5 × 3 × 2 × 2
Now, the same for 48:
24 × 2
12 × 2 × 2
6 × 2 × 2 × 2
3 × 2 × 2 × 2 × 2
Now, identify the common prime factors:
3 is found in both one time
2 is found in both two times
Multiply the factors that are found in both:
3 × 2 × 2 = 12
12 is thus the highest common factor
