Question

An acute triangle has side lengths 21 cm, X cm, and 2x cm. If 21 is one of the shorter side of the triangle, what is the greatest possible length of the longest side, rounded to the nearest 10th?

Answer 1

The triangle inequality tells us that the sum of the two shorter sides of a triangle must be greater than the third side.

Here, 21 cm is one of the shorter sides, and x cm must be the length of the other shorter side.

So using the triangle inequality,
21+x > 2x
or x<21 cm
To the nearest 0.1 cm, the greatest possible length of the longest side (2x) is 2*21-0.1 cm = 41.9 cm < 2x=42 cm.