Question

Two sides of a triangle have the following measure of 7,8.what is the range of possiable values for the 3rd side?

Answer 1

The third side of the triangle could be between 1 and 15 units, exclusive. This is because there is a theorem in geometry that states that, if you add 2 of a triangle's sides, the third side has to be less than the sum of the first two sides. This means that the third side has to be less than 8 + 7 = 15. So the third side is less than 15 units. This also means that the third side plus another side has to be greater than the last side. To find the minimum value, you take the smallest side, in this case, 7, and create an inequality. The inequality would be 7 + x [the third side] > 8. Solving this inequality, you get that x > 1. This means that 1 < x < 15. That is the range of values for the third side.