Chapter 15, Problem 18RP

To determine

To Find: The possible number of triangles that can be formed in the given data.

Answer to Problem 18RP

Only three.

Explanation of Solution

Given:

  

  $\text{an obtuse }\Delta \text{ABC with }a=6$

Formula Used:

  $\begin{array}{l}\text{In obtuse angle}\\ {\text{a}}^2>b^2+c^2\end{array}$

Calculation:

  $\begin{array}{l}{a}^2>b^2+c^2\\ 36>b^2+c^2\\ \text{The triangle inequalities}\\ b+c>a=6\\ b+6>c\\ c+6>b\\ \text{Possible values for }\\ \text{b=3; c=4}\\ \text{b=3; c=5}\\ \text{b=4; c=4}\end{array}$

Conclusion:

Thus, only three type of triangle is possible.