First, theory of triangle side requirements. Knowing two sides of one triangle, you can find a range of the length of the third side by only calculating the the sum and difference of the two known sides, the length of the third side has to be between the sum and difference. I tried out a few examples in geogebra, like i set it when both the sides are equal to 15, the max of the scale,The longest possible length is 29.9 reapeated, because it has to be smaller than 30, the sum of the two sides, the shortest possible is not really defined as one number, but it has to be very close to zero, the difference of the two sides.

1. If a triangle has sides of 21 and 24, how SHORT can the third side be? The shortest side it can be is the smallest number that is above the difference, which is 3, so i tried using a similar number on geogebra and the closest i got was 3.001.

2. If a triangle has sides of 21 and 24, how LONG can the third side be? The longest it can be is the number slightly less than the sum of the two numbers, which in this case, is 45, so the answer i got is 44.9 repeated.

3.Will side lengths of 20, 30, and 50 make a triangle? The side lengths 20 and 30 added up is the number 50, which is the side length of the thrid side. Refering to the theory i answered earlier, the third side has to be between the sum and the difference, 50 and 10 in this problem, so the answer is no.