Question

Which measures CANNOT be the side lengths of a triangle?

A. 10cm,4cm,13cm
B. 7cm,7cm,7cm
C. 2cm,15cm,16cm
D. 9cm,8cm,18cm

Answer 1

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Option D (9cm, 8cm, 18cm) cannot satisfy this condition and therefore cannot be the side lengths of a triangle.

Step-by-step explanation:

In order for three side lengths to form a triangle, they must satisfy the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's analyze each option:

1. Option A (10cm, 4cm, 13cm): 10cm + 4cm = 14cm, which is greater than 13cm. Therefore, this option can be the side lengths of a triangle.
2. Option B (7cm, 7cm, 7cm): All three sides are the same length, so this is an example of an equilateral triangle. This option can be the side lengths of a triangle.
3. Option C (2cm, 15cm, 16cm): 2cm + 15cm = 17cm, which is greater than 16cm. Therefore, this option can be the side lengths of a triangle.
4. Option D (9cm, 8cm, 18cm): 9cm + 8cm = 17cm, which is less than 18cm. Therefore, this option cannot be the side lengths of a triangle.

Based on the analysis, the answer is Option D (9cm, 8cm, 18cm).