Question

A triangle has 2 sides of length 15 and 19 what is the smallest possible whole number length for the 3rd side

Answer 1

We have a triangle with 2 sides of length 15 and 19.

We have to find the smallest possible whole number length for the 3rd side.

We can draw this as:

The third size is x.

If we reduce h, approaching to 0, x is minimized.

When h is very close to 0 (if h=0, the triangle cease to exist), the value of x can be written as a little bigger than the difference between the largest side (19) and the other side (15).

Then, x is, in the limit h-->0:

`x+15>19\Rightarrow x>19-15=4\Rightarrow x>4`

As x>4, the next whole number is 5.

NOTE: if x=4, the triangle does not exist, as there is no height or 3 angles.

Answer: The smallest whole number length for the 3rd side is 5.