Chapter 12.4, Problem 31E

To determine

To Find: The value of $t$ that make the triangle isosceles.

Answer to Problem 31E

  $6,8,and10.$

Explanation of Solution

Given: The length of the sides of the triangle are $3t,5t-12andt+20.$

Given: sides $3t,5t-12andt+20.$

To make it isosceles triangle

The first and second sides should be congruent legs.

Thus

  $\begin{array}{l}3t=5t-12\\ -2t=-12\\ t=6\end{array}$

Now

The second and third should be congruent legs.

  $\begin{array}{l}5t-12=t+20\\ 4t-12=20\\ t=8\end{array}$

Now

The first and third side could be congruent legs.

  $\begin{array}{l}3t=t+20\\ t=10\end{array}$

Hence, the possible values of $t$ are $6,8,and10.$