Question

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Mrs. O’Connor is creating a large square painting with the grade 8 art classes. The painting will be made of 24cm by 32cm rectangles covered with colored squares. They want these squares to be as large as possible, measured in whole numbers of centimeters.
Then they plan to arrange copies of the 24cm by 32cm rectangle to form a large square painting that measures the least possible whole number of centimeters.

What size will the small colored squares be?
How big will the painting be?

Answer 1

9514 1404 393

Answer:

• small squares: 8 cm square
• large painting: 96 cm square

Explanation:

The size of the small squares will be the greatest common divisor (GCD) of the dimensions 24 cm and 32 cm. We know these dimensions can be factored as ...

24 = 3×8

32 = 4×8

so the GCD is 8 cm.

The rectangles can be covered with squares that are 8 cm on a side.

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The dimensions of the painting will be the least common multiple of the rectangle dimensions. That is ...

LCM(24, 32) = 24×32/GCD(24, 32) = 24×32/8 = 96

The smallest square painting that can be made from these rectangles is 96 cm square.