Question

Which of the following are possible sidelengths for a triangle?A. 10, 12,3B. 14,8,3C. 15, 5,9

Answer 1

To solve this problem we must use the Triangle Inequality Theorem, which says:

In mathematical terms, if the triangle has sides of length a, b and c, the theorem states:

`\begin{gathered} a+b>c \\ b+c>a \\ c+a>b \end{gathered}`

We will verify which of the options satisfies the inequalities above.

A)

10 + 12 > 3 ✓

12 + 3 > 10 ✓

3 + 10 > 12 ✓

B)

14 + 8 > 3 ✓

8 + 3 < 14 ✖

3 + 14 > 8 ✓

C)

15 + 5 > 9 ✓

5 + 9 < 14 ✖

9 + 14 > 5 ✓

Answer

We see that the only sets of lengths that satisfy the three inequalities of the Triangle Inequality Theorem are the ones from option A.