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? 18.8 cm 24.2 cm 42.0 cm 72.7 cm

B. 24.2 cm

Step-by-step explanation:

We are given that,

A triangle has sides of measure x, 2x and 21 cm.

Using the Triangle Inequality Theorem, which states that, 'The sum of any two sides of the triangle is greater than the measure of the third side'.

As, 21 cm is the shorter side, we have the possible inequalities,

a). i.e. x < 21

b). i.e. i.e x > 7.

So, we have that, the range of the side of length x is

This gives us that,

The maximum value of the side of length x is less than 21 i.e. x < 21.

So, the maximum value of the side of length 2x is, 2x < 2×21 i.e. 2x < 42.

That is, the value of longest side is less than 42 (Since, 2x < 42).

Hence, the greatest possible length is 24.2 cm according to the options.

the first option is the answer.