Question

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

4x < h < 10x
10x < h < 4x
h = 4x
h = 10x

Answer 1

Use the triangle inequality: the third side must be less than the sum and greater than the difference of the other two sides.

|3x − 7x| < h < 3x + 7x ⇒ 4x < h < 10x.

So the correct expression is 4x < h < 10x (assuming x > 0 so sides are positive).