Chapter 3.4, Problem 18WE

(a)

To determine

To find: The value of t that make the given triangle as isosceles.

Answer to Problem 18WE

The value of $t$ that will make this triangle isosceles is $t=8$

Explanation of Solution

Given information:

Length of sides of triangle:

  $3t,5t-12$ and $t+20.$

In an isosceles triangle, two sides are equal.

Let us equate two sides of this triangle.

  $\begin{array}{l}5t-12=t+20\\ \begin{array}{cc}4t& =20+12\\ 4t& =32\\ t& =8\end{array}\end{array}$

So $t=8$ is that value of $t$ that will make this triangle isosceles.

Hence, $t=8$

(b)

To determine

To find: The value of t that make given triangle equilateral.

Answer to Problem 18WE

There is no value of $t$ that will make this triangle equilateral.

Explanation of Solution

In an equilateral triangle, all the sides are equal. So let us take two sides of this triangle and equate them.

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

Substitute this value of $t$ in the third side.

  $\begin{array}{l}t+20=6+20\\ t=26\end{array}$

Put the value of $t$ in all sides and get 18,18,26 length of sides, which does not represent that the triangle is equilateral. Therefore, there is no value of $t$ that will make this triangle equilateral.