Chapter 15.2, Problem 13PSB

To determine

To Find: The shortest length of a triangle.

Answer to Problem 13PSB

The shortest side is 2cm. long.

Explanation of Solution

Given:

The sum of sides of a triangle is 8cm.

Formula Used:

Exterior Angle of a triangle is always greater than its remote interior angles.

Angle-Sum theorem: Sum of interior angle of a triangle is 180.

Calculation:

  $\begin{array}{l}\text{all the possible sizes}\\ \text{1,1,6}\\ \text{⇒}\text{1+1<}6\\ \text{its not a triangle}\\ \text{1,2,5}\\ \text{⇒}\text{1+2}<5\\ \text{its not a triangle}\\ 1,3,4\\ \text{⇒}1+3=4\\ \text{its not a triangle}\\ 2,2,4\\ \text{⇒}2+2=4\\ \text{its not a triangle}\\ 2,3,3\\ \text{⇒}2+3>3\\ \text{this forms a triangle}\text{.}\\ \text{and in this the shortest side is 2cm}\text{.}\end{array}$

Conclusion:

Thus, Cutting the pieces in 2,3,3 will make a triangle.