A rectangular box has integer side length in the ratio 1:3:4. Which of 48, 56, 64, 96, 144 could be the volume of the box?

amc81012 Jun 16, 2021

#1**+2 **

*A rectangular box has integer side length in the ratio 1:3:4. Which of 48, 56, 64, 96, 144 could be the volume of the box?*

A box 2 x 6 x 8 would have volume **96 units ^{3}**.

The wording of the problem implies that there's only one answer, so I didn't check any of the others.

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Guest Jun 16, 2021

#2

#4**+3 **

Hi, Techno! You misunderstood the question.

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A **rectangular box** has integer side length in the ratio 1:3:4. Which of 48, 56, 64, 96, 144 could be the volume of the box?

1 : 3 : 4 = 2 : 6 : 8 = 3 : 9 : 12

1 * 3 * 4 = 24

2 * 6 * 8 = 96 Only the volume of 96 u^{3} is possible with the given integer side length ratio!!!

3 * 9 * 12 = 324

jugoslav
Jun 16, 2021

#5**0 **

Thanks, Jugoslav. I'm the "guest" who gave the first answer up there. I knew Techno's answer was wrong, but I was reluctant to point that out. For one reason, the inaccuracy is obvious. But the main reason was that I, as having given the correct answer, didn't want to be the one to b**w the whistle. I'm glad you came along to clear up the matter. ~Ron

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Guest Jun 16, 2021