Question

The lengths of two sides of a triangle are 26 meters and 48 meters. If x is the the third side, fill in the blank to solve for the possible range of the third side._____ meters

Answer 1

The triangle inequality says that in any triangle, the sum of any two sides is always greater than the third side.

In other words,

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

Now in our case, two sides are given and if we call a = 26m and b = 48m, the above gives

$\begin{gathered} 26+48>c \\ 26+c>48 \\ 48+c>26 \end{gathered}$

which solve for c to give

$\begin{gathered} 74>c \\ c>22 \\ c>-22 \end{gathered}$

Now, between c>22 and c> -22, the inequality c> 22 encompasses everything and so we disregard c> -22 and choose c> 22; hence, we have

$\begin{gathered} 74>c \\ c>22 \end{gathered}$

this says c is less than 74 but greater than 22, meaning

[tex]22mwhich is our answer!