Question

Hello I need help the question asks ; two sides of a triangle are 6mm and 9 mm long. The possible lengths for the remaining side of the triangle , s, can be found using the compound inequality below

Answer 1

D

1) We need to remind ourselves of the Triangular inequality so that we can tackle this question:

$a+b>c,b+c>a,c+a>b$

Simply put, the sum of two sides must be greater than one of their sides.

2) Note that we were told that two of those legs have the size of 6 and 9

So, we can write out this:

$\begin{gathered} 6+s>9 \\ s>9-6 \\ s>3 \\ 6+9>s \\ s<15 \end{gathered}$

3) Therefore, we can see that 3

Thus, the answer is D