Is the quotient of two perfect squares always a perfect square? Explain your reasoning.

Also, two squares are drawn. The smaller square has an area of 256 square meters. The areas of the two squares have a ratio of 4:9. What is the side length \( s \) of the larger square?

The side length of the larger square is 24 meters, found by setting up a proportional relationship between the side lengths of the two squares and solving for the unknown. ;

Answered by EllaMarija | 2024-06-18

No, the quotient of two perfect squares is not always a perfect square. take 16/9 for example, it equals 1.77777777(bar notation), which is most certainly not a perfect square.
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If the area of the smaller square is 256, then its side length is 16. Putting 16 into the ratio, the new ration would be 16:36 because both the 4 and 9 are multiplied by 4. So, the side length of the larger triangle is 36.

Answered by Hiirene | 2024-06-24

The quotient of two perfect squares is not always a perfect square, as shown with the example 16 and 9. The side length of the larger square, given the areas' ratio of 4:9, is 24 meters. The area of the smaller square is 256 square meters, leading to a larger square area of 576 square meters.
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Answered by Hiirene | 2024-12-26