Question

two sides of a triangle have the following measures. Find the range of possible measures for the third side. 11, 7

Answer 1

The given sides are 11 and 7.

So from the pythagoras theorem, when we take the unknown as base or altitude.

$\begin{gathered} 11^2=7^2+x^2 \\ 121=49+x^2 \\ 72=x^2 \\ x=8.45 \end{gathered}$

When the unknown is hypotenuse,

$\begin{gathered} x^2=121+49=170 \\ x=\sqrt[]{170}=13.03 \end{gathered}$

So the range of x is,

$8.45\leq x\leq13.03$