Question

You have a wooden board that measures 54 centimeters by 90 centimeters. You want to cut the board into identical square pieces with integer side lengths and use all of the wood.

a. Make a sketch of the board. Find three possible side lengths for the squares.
b. What is the largest side length you can choose? Explain.
c. How many square pieces will you have?

Answer 1

Answer: a. Here is a sketch of the wooden board with dimensions 54 cm by 90 cm:

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Possible side lengths for the squares could be:

9 cm (since both 54 and 90 are divisible by 9)

6 cm (since both 54 and 90 are divisible by 6)

3 cm (since both 54 and 90 are divisible by 3)

b. To find the largest side length of the squares, we need to find the greatest common divisor (GCD) of 54 and 90. The GCD of 54 and 90 is 18. Therefore, the largest side length you can choose is 18 cm. This is because 18 cm is a divisor of both 54 and 90, ensuring that the board can be evenly divided into square pieces of that size.

c. To find the number of square pieces, we divide the dimensions of the board by the side length of the squares. In this case, if we use 18 cm as the side length, we can divide both 54 cm and 90 cm by 18 cm.

Number of square pieces = (54 cm ÷ 18 cm) * (90 cm ÷ 18 cm) = 3 * 5 = 15

Therefore, you will have 15 square pieces if you choose a side length of 18 cm.

Step-by-step explanation: Hope this helps :D