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# What is the length of hypotenuse K?

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What is the length of hypotenuse K? [#permalink]  13 Oct 2017, 11:50
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100% (04:48) correct 0% (00:00) wrong based on 6 sessions
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What is the length of hypotenuse K?

[Reveal] Spoiler: OA
7.8

Last edited by Carcass on 12 Apr 2019, 11:25, edited 2 times in total.
Edited by Carcass
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Re: Similar Triangle [#permalink]  13 Oct 2017, 12:22
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Re: Find the length of hypotenuse K [#permalink]  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]  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"
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Re: Find the length of hypotenuse K [#permalink]  20 Jan 2019, 17:22
Ans 7.8
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Re: Find the length of hypotenuse K [#permalink]  12 Apr 2019, 09:36
Any more explanations for this question?
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Re: Find the length of hypotenuse K [#permalink]  12 Apr 2019, 21:07
LT2018 wrote:
Any more explanations for this question?

Plz see the diag. below

As

Now the left hand triangle is a 5-12-13 triangle (Pitagorean triplet) ( it can also be dudced by pythogorus theorem as the unkown side = \sqrt{13^2 - 12^2} = 5)

Since the left part of the triangle has got the base 5, hence the base of the other triangle = 12.2 - 5 = 7.2

Now both triangles are similar ( Angle - angle -angle)

and hence the side can be deduced in the form:

$$\frac{7.2}{12}= \frac{k}{13}$$

or $$k = 7.8$$
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Re: Find the length of hypotenuse K   [#permalink] 12 Apr 2019, 21:07
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