Questions on Geometry: Triangles answered by real tutors!

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Question 148450: 4. If a triangle has a 5-inch side and a 6-inch side, how can it be similar to a triangle with a 4 and 8 inch side? Find all possible examples. Check that examples really ARE triangles.

: 4. If a triangle has a 5-inch side and a 6-inch side, how can it be similar to a triangle with a 4 and 8 inch side? Find all possible examples. Check that examples really ARE triangles.


Answer by jim_thompson5910(9217) About Me  (Show Source):
You can put this solution on YOUR website!

Once again, a drawing helps:


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I'm not real sure how to go about this problem, but I would start by pairing up corresponding sides. So side "5" would correspond to side "4", side "5" would correspond to side "8", side "5" would correspond to side "y", etc. This pairing goes on for quite a while. So here are the pairs that I've drawn up

5/4=6/y Solution y=24/5
5/4=6/8 No Solution
5/8=6/y Solution y=48/5
5/8=6/4 No Solution
5/y=6/8 Solution y=20/3
5/y=6/4 Solution y=10/3
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6/4=5/y Solution y=10/3
6/4=5/8 No Solution
6/8=5/y Solution y=20/3
6/8=5/4 No Solution
6/y=5/8 Solution y=48/5
6/y=5/4 Solution y=24/5
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x/4=5/y Infinite Solutions
x/4=5/8 Solution x=5/2
x/8=5/y Infinite Solutions
x/8=5/4 Solution x=10
x/y=5/8 Infinite Solutions
x/y=5/4 Infinite Solutions
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This list is probably far from exhaustive, but it gives you an idea of the sides that the triangles can take. To see if a triangle is formed from 3 sides, you must test to see if the sum of any two given sides are greater than the length of the third side (you must test this for all three sides and for every possible case. So the problem gets a lot longer).

Also, to find every solution has stumped me. From the list, it's hard to tell for sure if I've listed every case. Sorry for the trouble.