I have a flat piece of plywood that measures 45 inches in width and 75 inches in length. I want to cut the board into identical square pieces with the integer side lengths and use the entire piece of wood. What are the dimensions (width & length) of each identical piece? Please include an explanation with the answer.
They could be either 5 by 5 or 15 by 15.
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I have a flat piece of plywood that measures 45 inches in width and 75 inches in length. I want to cut the board into identical square pieces with the integer side lengths and use the entire piece of wood. What are the dimensions (width & length) of each identical piece? Please include an explanation with the answer.
To cut the plywood into identical square pieces and use the entire piece of wood, we need to find the largest perfect square that can evenly divide both the width and length of the plywood.
To do this, we can find the greatest common divisor (GCD) of the width and length. The GCD represents the largest square that can evenly divide both dimensions.
In this case, the GCD of 45 and 75 is 15. This means that the largest square that can evenly divide both dimensions is a square with sides measuring 15 inches.
Therefore, each identical square piece will have dimensions of 15 inches by 15 inches.