Triangle trusses

Calculus Level 5

△ A B C \triangle ABC is right angle triangle, where A B = 300 and B C = 400 AB = 300 \ \text{and} \ BC = 400 , Find the length l l of the blue link.

Give your answer as ⌊ l ⌋ \lfloor l \rfloor .


The answer is 25.

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Mark Hennings
Sep 4, 2018

We have a large collection of similar right-angled triangles here, and so the n n th link number is x n = 300 ( 4 5 ) 2 n − 1 x_n = 300\big(\tfrac45\big)^{2n-1} . We want ⌊ x 6 ⌋ = ⌊ 300 ( 4 5 ) 11 ⌋ = ⌊ 25.769803776 ⌋ = 25 \lfloor x_6\rfloor = \big\lfloor 300\big(\tfrac45\big)^{11}\big\rfloor = \lfloor 25.769803776\rfloor = \boxed{25}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Here's how it looks with 11 11 links in place

That 11 11 th link looks a lot shorter than 25 25

Michael Mendrin - 2 years, 9 months ago

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This diagram has way more than 11 link numbers in it. There are at least 8 orange lines here, and we only need the sixth.

Mark Hennings - 2 years, 9 months ago

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Okay, I think I see the whole problem right there... it simply says "find the length of the blue link" ...oh, wait... that has been revised. Originally it asked for link 11 11 , now it's marked 6 6 . It's all A-Okay now! My faith in you has been restored.

Michael Mendrin - 2 years, 9 months ago

I think the reports can be eliminated because they all are correct, but refer to a problem that no longer exists. The problem was changed after the appearance of the reports. Ed Gray

Edwin Gray - 2 years, 9 months ago

0 pending reports

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