perplexus.info :: Shapes : Triangle in a triangle

Triangle in a triangle (Posted on 2017-08-28)

If you have a triangle with sides A<B<C
and a smaller triangle with sides a<b<c,
where a<A, b<B, and c<C,
will the smaller triangle always fit entirely within the larger one?

No Solution Yet Submitted by Jer

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re: How about this one?

| Comment 3 of 4 |

(In reply to How about this one? by Larry)

Nice!

You don't even need a triangle that extreme. A triangle with sides 3,3,5 has its shortest altitude of sqrt(11)/2 = 1.658.

The equilateral triangle 2,2,2 has all its sides smaller and has altitudes of sqrt(3) = 1.732, which won't fit in the 3,3,5 triangle.

Posted by Brian Smith on 2017-08-28 13:23:33

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