Which three lengths could be the lengths of the sides of a triangle?

Option D is correct.

Step-by-step explanation:

We use the following result:

If sum of two sides of a triangle is greater than third side then Triangle is possible with those sides.

Option A).

a = 21 , b = 7 , c = 7

a + b = 21 + 7 = 28 > c

b + c = 7 + 7 = 14 < a

So, These length cannot be lengths of the sides of the triangle.

Option B).

a = 20 , b = 6 , c = 8

a + b = 20 + 6 = 26 > c

b + c = 6 + 8 = 14 < a

So, These length cannot be lengths of the sides of the triangle.

Option C).

a = 15 , b = 5 , c = 20

a + b = 15 + 5 = 20 = c

So, These length cannot be lengths of the sides of the triangle.

Option D).

a = 9 , b = 14 , c = 22

a + b = 9 + 14 = 23 > c

b + c = 14 + 22 = 36 > a

a + c = 9 + 22 = 31 > b

So, These length can be lengths of the sides of the triangle.

Therefore, Option D is correct.

The equation is unsolvable when the 'a' variable is in it, so if we take it out, then all of them would make the equation open up.

Sorry for not giving a definite answer, but that is what I got.

Hope that this helps!