Question

Which of the following sets of numbers could not represent the three sides of a triangle?

A) {15, 21, 33}
B) {13, 27, 38}
C) {15, 27, 43}
D) {6, 15, 20}

Answer 1

To answer which set of numbers could not represent the sides of a triangle, the Triangle Inequality Theorem is applied. Set C, which is {15, 27, 43}, fails this theorem because the sum of the shortest two sides is not greater than the length of the longest side.

Step-by-step explanation:

The student's question asks which set of numbers could not represent the sides of a triangle. To determine if a set of numbers can be the sides of a triangle, the Triangle Inequality Theorem is used, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

• Set A {15, 21, 33} passes the theorem as 15 + 21 > 33, 21 + 33 > 15, and 15 + 33 > 21.
• Set B {13, 27, 38} also passes as 13 + 27 > 38, 13 + 38 > 27, and 27 + 38 > 13.
• Set C {15, 27, 43} does not satisfy the theorem because 15 + 27 is not greater than 43.
• Set D {6, 15, 20} passes the theorem as 6 + 15 > 20, 6 + 20 > 15, and 15 + 20 > 6.

Therefore, set C is the one that could not represent the sides of a triangle.