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Find the length of hypotenuse K

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Intern
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Find the length of hypotenuse K [#permalink] New post 13 Oct 2017, 11:50
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Find the length of hypotenuse K
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Director
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Re: Similar Triangle [#permalink] New post 13 Oct 2017, 12:22
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Re: Find the length of hypotenuse K [#permalink] New post 15 Oct 2017, 01:57
The solution holds anyway the question is posted so I go on.

Let's recognize that the left hand triangle is a 5-12-13 triangle (Pitagorean triplet) so that we can derive the horizontal leg of the right hand side triangle as 12.2-5 = 7.2.

Now, let's notice that the two triangles are similar: they have the three angles equal among them so that the ratio between legs is 12/7.2

Then, since all the other sides must maintain the same ratio, we know that 12/7.2 = 13/k, from which we can derive k = 7.8
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Re: Find the length of hypotenuse K [#permalink] New post 15 Nov 2017, 14:09
IlCreatore wrote:
The solution holds anyway the question is posted so I go on.

Let's recognize that the left hand triangle is a 5-12-13 triangle (Pitagorean triplet) so that we can derive the horizontal leg of the right hand side triangle as 12.2-5 = 7.2.

Now, let's notice that the two triangles are similar: they have the three angles equal among them so that the ratio between legs is 12/7.2

Then, since all the other sides must maintain the same ratio, we know that 12/7.2 = 13/k, from which we can derive k = 7.8



how can you make sure "they have the three angles equal among them so that the ratio between legs is 12/7.2"
Re: Find the length of hypotenuse K   [#permalink] 15 Nov 2017, 14:09
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Find the length of hypotenuse K

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