Question

The lengths of two sides of a triangle are 11 and 20. Which of the following must be true about the third side, n?

a) n > 9
b) n < 20
c) 9 < n < 31
d) 9 < n < 20

Answer 1

The lengths of two sides of a triangle are given as 11 and 20. The length of the third side must be greater than 9 but less than 31 due to the triangle inequality theorem. Therefore, the correct answer is 9 < n < 31.

Step-by-step explanation:

The student is asking about the possible lengths of the third side of a triangle when the lengths of the other two sides are known. This is a problem related to the triangle inequality theorem, which in mathematics states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Using this theorem, if we have two sides of lengths 11 and 20, the third side must be longer than the difference of the two lengths (20 - 11 = 9) but less than the sum of the two lengths (20 + 11 = 31). Therefore, the third side n must satisfy 9 < n < 31.