Using the Pythagorean Theorem, do a^2 + b^2 = c^2. The biggest number has to be the hypotenuse, so 10.7 would be the hypotenuse. Therefore, 5.5^2 and 3.2^2 have to equal 10.7^2.
To start, find the square of both 5.5 and 3.2.
5.5^2 = 30.25
3.2^2 = 10.24
Now add them together to give you:
30.25 + 10.24 = 40.49.
Finally, find the square root of 40.49. If it is 10.7, then the 3 measurements can be side lengths. If not, they cannot all be side lengths.
This yields 6.36317530797. Since this is NOT 10.7, the 3 measurements cannot be side lengths of a triangle.
Hope this helps! :)
