Question

An acute triangle has side lengths 21 cm, x cm, and 2x cm. if 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

Answer 1

C. 42.0

Explanation:

Answer 2

Given that the sides of the acute triangle are as follows:
21 cm
x cm
2x cm

Stated that 21 cm is one of the shorter sides of the triangle2x is greater than x, so it follows that 2x MUST be the longest side


For acute triangles, the longest side must be less than the sum of the 2 shorter sides
Therefore, 2x < x + 21cm
2x – x < 21cm
x < 21cm

If x < 21cm, then 2x < 42cm
Therefore, the longest possible length for the longest side is 42cm