Question

A triangle has sides 45, 4x and 2x−4. What is the possible range of x?

Answer 1

x>2

The greatest possible value cannot be stated as it is not mentioned whether it is a right angled triangle, which is hypotenuse, or which is the smallest/largest side.

Answer 2

49/6 < x < 41/2.

Explanation:

In any triangle, each side is shorter than the sum of two other sides.

It gives three independent inequality

45 < 4x + (2x-4), (1)

4x < 45 + (2x-4), (2)

2x-4 < 45 + 4x. (3)

From (1), 6x > 45 + 4 = 49 ---> x > 49/6

From (2), 2x < 45 - 4 = 41 ---> x < 4/2

From (3), 2x > -4 - 45 = -49 ---> x > -49/2