Mario wants to cut two pieces of material into equal-sized squares with no materials wasted. One piece measures 12 in. by 36 in. In The other measures 6 in. by 42 in. What is the largest size square that he can cut
A side can not be longer than 6 inches.
Luckily 12, 36 and 42 are exact multiples of 6.
To find the largest size square that Mario can cut from the given pieces of material, we need to determine the greatest common divisor (GCD) of the dimensions.
For the first piece:
Length = 12 in., Width = 36 in.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
From the common factors, we can see that the GCD of 12 and 36 is 12.
For the second piece:
Length = 6 in., Width = 42 in.
Factors of 6: 1, 2, 3, 6
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
From the common factors, we can see that the GCD of 6 and 42 is 6.
Therefore, the largest size square that Mario can cut from the given pieces of material is a square with dimensions of 6 inches by 6 inches.
To find the largest size square that Mario can cut from the two pieces of material, we need to determine the greatest common divisor (GCD) of the dimensions of the pieces. The GCD will represent the maximum size square that can be cut from both pieces without any wastage.
For the first piece of material measuring 12 in. by 36 in., we can factor out the GCD by dividing both dimensions by their common factors, as follows:
12 in. = 2 × 2 × 3
36 in. = 2 × 2 × 3 × 3
Thus, the GCD of these dimensions is 2 × 2 × 3 = 12
For the second piece of material measuring 6 in. by 42 in., we can factor out the GCD by dividing both dimensions by their common factors, as follows:
6 in. = 2 × 3
42 in. = 2 × 3 × 7
Thus, the GCD of these dimensions is 2 × 3 = 6.
Now that we have identified the GCD of both pieces as 6, we know that the largest square that Mario can cut from both pieces without wastage will measure 6 in. by 6 in.
Therefore, the largest size square that Mario can cut from the given pieces of material is 6 inches by 6 inches.