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The banana problem

There is a SQUARE field and 44 BANANA trees are planted across the square field. Find the peremeter of that square field, if the distance between 2 BANANA tree is 2 metre.

Note by Jeet Dubey
3 years, 11 months ago

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88 Stelvio Andreatta · 1 year, 8 months ago

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4 Banana trees are planted ONE at each corner of a square. and 10 trees are planted at each side between two corners of a side so Perimeter of the square field=4+(10*4)=44 meter Nasir Mehmood Alam · 3 years, 10 months ago

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352 m is right i suppose considering question is right ! 44 banana across the field (assuming the line of 44 bananas parallel to one of the side) having 2 metre between each tree so length of one side comes to 88m . Since perimeter is asked we have to take addition four time because it is square, so 88*4=352. Jeet Jajal · 3 years, 10 months ago

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Perimeter is 88 m. 12 banana trees per side, 22 metre per side. Luca Bernardelli · 3 years, 11 months ago

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@Luca Bernardelli Why are there 12 banana trees per side? Calvin Lin Staff · 3 years, 11 months ago

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@Calvin Lin I thought the 44 trees are in the perimeter...12 per side with 4 in commons in the corners. This is my only way to interpret the problem so that it's logical... Luca Bernardelli · 3 years, 11 months ago

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@Luca Bernardelli That's certainly a valid interpretation, given the ambiguity in the question. Thanks for explaining! Calvin Lin Staff · 3 years, 11 months ago

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@Calvin Lin No problem :) Luca Bernardelli · 3 years, 11 months ago

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44 is not a square number so the field can't be square Tan Li Xuan · 3 years, 11 months ago

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@Tan Li Xuan I agree that this question doesn't make much sense, and that 144 (likely a typo) would be a much better interpretation.

However, you're making the assumption that the banana trees must be planted parallel to the sides of the field, which is not necessary. Hence, an interpretation of this problem (which likely isn't the one originally intended) could be to find the minimum area of a field that contains exactly 44 banana trees. Calvin Lin Staff · 3 years, 11 months ago

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@Calvin Lin If Jeet D intended to type 144,then the answer would be the same as Luca B's answer.Otherwise it should be \( 6 \times 2m \times 4=48m \) because 49 is the smallest square number larger than 44 and \( \sqrt{49}=7\) Tan Li Xuan · 3 years, 11 months ago

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@Tan Li Xuan Not quite. This is actually much more interesting. You are still making the same assumption that the banana trees must be planted parallel to the sides of the field.

For example, if we only wanted 2 trees, then your approach will require a square field of side length 2, which has 4 banana trees on the corners. Whereas, if you take the 'diamond', you can see that a square field of side length \( \sqrt{2} \) is sufficient, with 2 banana trees on the opposite corners. Can you find an argument to show that this is the minimum length possible?

What happens in the case for 3 banana trees? Can we also do it with a square field of side length \( \sqrt{2} \)? If not, what is the minimum length?

What happens in the case for 4 banana trees? Is the minimum length 2? Can we not do any better? Why, or why not?

What happens in the case for 44 banana trees? Calvin Lin Staff · 3 years, 11 months ago

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@Tan Li Xuan Double interpretation with same result LOL Luca Bernardelli · 3 years, 11 months ago

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please explain Jeet Dubey · 3 years, 11 months ago

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