Question

10, 18, and x are the measure of sides of a triangle. Find the range of values of x.

Answer 1

Using triangle inequality theorem, we can say 'sum of any two sides of a triangle is greater than the third side'.

So we can write,
10 + 18 > x
That is, x < 28

let assume a,b and, c as three sides of a triangle.
then a + b > c, also b - a < c

The difference between any two sides should be less than the other side.

So, 18 - 10 < x
x > 8

Hence the range of x will be,
8 < x < 28