A triangle has a side length of 11, and a side length of 17. The third side length is also a positive integer. How many different possible values are there for the third side length? (Assume that the triangle is non-degenerate.)

21 different positive integers could be the length of the third side.

Step-by-step explanation:

By triangle inequality, the sum of two sides cannot be greater than the third.

This means that the third side is between (17-11)=6 and (17+11)=28.

How many integers are between there? You could write them out and count them!

Or!

The highest integer the third side can be is 27 and the lowest integer it can be is 7.

So 27-7+1=20+1=21.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer: 8

step-by-step explanation: