Find the range for the measurement of the third side of a triangle given two sides are 8.6 km and 14.5 km

Third side of the triangle should be larger than 5.9 km, and smaller than 23.1 km

Step-by-step explanation:

Let's examine the two extreme cases for any possible triangle that has two known sides and one larger than the other one. The attached figure tries to represent those extreme cases.

In the first depicted case, the third side (shown in red) is barely larger than the difference between the known sides (shown in green). So for this case we have that the third side must be > 14.5 km - 8.6 km

that is : third side > 5.9 km

In the opposite case, when we place the two known sides (shown in green) almost opposite to each other, the measure of the third side is almost (but not quite) the addition of the known sides.

Then this third side is < 14,5 km + 8.6 km = 23.1 km

Conclusion:

5.9 km < third side <23.1 km

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step-by-step explanation: