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Re: Similar Triangle [#permalink]
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Re: Find the length of hypotenuse K [#permalink]
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]
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]
Ans 7.8
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Re: Find the length of hypotenuse K [#permalink]
Any more explanations for this question?
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Re: Find the length of hypotenuse K [#permalink]
pranab01 wrote:
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 \(k = 7.8\)



How can you deduce side with 12 and side with k are the respective same side of the two different triangles? I initially did (5/7.2)= (13/k)
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Re: Find the length of hypotenuse K [#permalink]
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SusieSushi wrote:
pranab01 wrote:
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 \(k = 7.8\)



How can you deduce side with 12 and side with k are the respective same side of the two different triangles? I initially did (5/7.2)= (13/k)


Yes, you can get it incorrect, if you don't look into the diagram.

Kindly look into the diagram in the previous post,
For the smaller triangle the side 7.2 is between the angles: (90 - x) and 90

For the larger triangle , side 12 is between the angles: (90 - x) and 90

the side of length 5 is between the angles : 90 and x

The ratio for similar triangles are in the same corresponding sides and remember: Diagram are not drawn to scale
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Re: Find the length of hypotenuse K [#permalink]
pranab01 wrote:
SusieSushi wrote:

Yes, you can get it incorrect, if you don't look into the diagram.

Kindly look into the diagram in the previous post,
For the smaller triangle the side 7.2 is between the angles: (90 - x) and 90

For the larger triangle , side 12 is between the angles: (90 - x) and 90

the side of length 5 is between the angles : 90 and x

The ratio for similar triangles are in the same corresponding sides and remember: Diagram are not drawn to scale


I could be wrong here but couldn't I just switch where you had placed the x and the x-90 on one of the triangles and the relationship would still hold? Except if I were to switch it now the reference for the respective side would be wrong. I think thats how I initially got this wrong.
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Re: Find the length of hypotenuse K [#permalink]
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SusieSushi wrote:

I could be wrong here but couldn't I just switch where you had placed the x and the x-90 on one of the triangles and the relationship would still hold?


Iam not sure, what you meant?

you can't replace "x" with "90-x" and vice versa, as this will invalidate the question given. You have to approach based on what is given.


But, if you think ur approach is correct, just post it here.
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Re: Find the length of hypotenuse K [#permalink]
pranab01 wrote:
SusieSushi wrote:

I could be wrong here but couldn't I just switch where you had placed the x and the x-90 on one of the triangles and the relationship would still hold?


Iam not sure, what you meant?

you can't replace "x" with "90-x" and vice versa, as this will invalidate the question given. You have to approach based on what is given.


But, if you think ur approach is correct, just post it here.



I am still not sure how to go about this question without first knowing the answer. I just know I got the question wrong too by doing this: a) I had the position of 90-X and X switched for the left triangle in pranab01's diagram, b) came by this equation instead as a result (5/7.2) = (13/k). Perhaps I am forgetting a geometric rule here?

Originally posted by SusieSushi on 25 Oct 2019, 22:26.
Last edited by SusieSushi on 27 Oct 2019, 14:34, edited 1 time in total.
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Re: What is the length of hypotenuse K? [#permalink]
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Sorry Sir,

This is a forum in which you have to format your answer as text, If all of us start to post photography of the solution, turns out, this board will become a mess.

I appreciate your effort and the will to learn and clarify your doubts. However, please post as normal reply your questions.

As a text, typing.

Best Regards
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Re: Find the length of hypotenuse K [#permalink]
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SusieSushi wrote:
pranab01 wrote:
SusieSushi wrote:

I could be wrong here but couldn't I just switch where you had placed the x and the x-90 on one of the triangles and the relationship would still hold?


Iam not sure, what you meant?

you can't replace "x" with "90-x" and vice versa, as this will invalidate the question given. You have to approach based on what is given.


But, if you think ur approach is correct, just post it here.



I am still not sure how to go about this question without first knowing the answer. I just know I got the question wrong too by doing this (perhaps I am forgetting a geometric rule here?)


I will echo @Carcass words, please read the rules of posting::Rules for Posting
For the problem, you have not taken the angle between the side of length k and length 13. It is given 90 degree in the question.
Moreover, the straight line (line of length 5 and length 7.2) don't makeup 180 degree (90-x, 90, 90-x)
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Re: What is the length of hypotenuse K? [#permalink]
Carcass wrote:
Sorry Sir,

This is a forum in which you have to format your answer as text, If all of us start to post photography of the solution, turns out, this board will become a mess.

I appreciate your effort and the will to learn and clarify your doubts. However, please post as normal reply your questions.

As a text, typing.

Best Regards



That makes sense, I had not considered that. Sorry! I will go ahead and reformat the post
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Re: What is the length of hypotenuse K? [#permalink]
If we didn't know that it was a 5,12,13 triangle with 30,60,90..would we still be able to tell that those are similar triangles?
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Re: What is the length of hypotenuse K? [#permalink]
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nerd77 wrote:
If we didn't know that it was a 5,12,13 triangle with 30,60,90..would we still be able to tell that those are similar triangles?


Hi,

Not sure what you are trying to say

The 2 \(\triangle\)s are similar by Angle-Angle-Angle .

Here is a link to similar triangle, hope it help you

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Re: What is the length of hypotenuse K? [#permalink]
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Re: What is the length of hypotenuse K? [#permalink]
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