logic question?

Question

Two similar triangles have two of their sides the same length. If the length of the third sides differ by 20141, what is the sum of the third sides? (Note: all sides are positive integers).

the wording has me confued. anyone want to try it and explain their answer?

Edit: the triangles are similar, and two sides equals two sides of the other triangles, so yeah, both isosceleses

its the second condition nate mentioned

>>So you are saying that 4 of the 6 sides of those triangles are equal?

Yes, two similar isosceleses

There are two conditions that could be depending on how you read the problem. Thats the actual wording of the problem too.

Answer 1

I'm not sure this one has a solution--but let me tell you why I have come to that conclusion.

Remember that similar triangles have the same shape--the angles are the same size. That means that ratios between the sides of the triangles will remain constant--the longest side of the larger triangle divided by the longest side of the smaller triangle will give the same result as the shortest side of the larger triangle divided by the shortest side of the smaller triangle.

We also know that two sides of one of the triangles are the same length as two sides of the other. This CANNOT mean that we have two isoceles triangles--because the difference in lengths for the third legs would make it impossible for the triangles to be similar.

So here's what I think the problem is trying to tell us. The larger triangle has three sides--one long, one medium, one short. The smaller triangle also has three sides--one long, one medium, one short. And what we know is that the medium side of the larger triangle is the same length as the longest side of the smaller triangle--also that the shortest side of the larger triangle is the same length as the medium side of the smaller triangle. So the difference of 20141 is between the longest side of the larger triangle and the shortest side of the smaller triangle.

That seems to make sense of the wording of the problem. The only difficulty is that there is no solution in integers. Because of the constant ratios between the sides we are considering, this would have to mean that an^3 - a = 20141 (where a is the shortest side of the smaller triangle and n is the ratio factor for the sides of these triangles)--and there are no solutions where both a and n are integers.

Did you copy the problem down wrong?

Answer 2

This can be solve, but I need to know some more info first.

Does "two of their sides the same length" mean that these are two isosceles triangles (2 of the sides of one triangle are equal) or does that mean side A of one triangle equals side A of the other?r

Edit: So you are saying that 4 of the 6 sides of those triangles are equal?

Answer 3

Hmm...

The sides can't be corresponding...

So the "second side of the first triangle" must equal the "first side of the second triangle", and the "third side of the second triangle must equal the "second side of the second triangle".

Hmm...

The sides differ by 20141, and one is the other times the third power of something...

x + 20141 = xy³

Try finding y...
y³ = (x + 20141) / x
y = cubrt(1 + 20141 / x)

Hmm...

THere is no unique solution...

Answer 4

Ok.. as I read it.. it does not have to be isoceles triangles... example.. a triangle with sides a, b, c... and another triangle with sides of (b, c, d)... or (a, c, d), or (a, b, d)... you get the idea...

so... in this case... there may be a unique answer... how to get the answer is a different answer.. hehe

Answer 5

this is a tough one. unless there's a trick about isosceles triangles that i cant remember i would have to just keep plugging values in until I get difference provided. it would take me a long time.

Answer 6

SIMILAR triangles can't have the same sides, only the same ANGLES. :/

Answer 7

The Giraffe.

Answer 8

It is not possible without the proper info

Answer 9

no, i would say the earth is flat.