Chapter 1, Problem 6CA

To determine

To calculate the length of the shortest side.

Answer to Problem 6CA

3 inches

Explanation of Solution

Given:

  $\text{Perimeter of triangle = 13 inches}$

  

Formula used:

  $\text{Perimeter of triangle = sum of the sides of the triangle}$

Calculation:

From the given figure, the sides of the triangle are $(x-5)$ , $\frac{x}{2}$ and 6 inches.

  $\text{Perimeter of triangle = sum of the sides of the triangle}$

  $\begin{array}{l}\text{Perimeter of triangle =}(x-5)+\frac{x}{2}\text{+6 }\\ \Rightarrow 13\times 2=2\times (x-5)+x+2\times 6\\ \Rightarrow 26=2x-10+x+12\\ \Rightarrow 26=3x+2\\ \Rightarrow 26-2=3x\\ \Rightarrow 24=3x\\ \Rightarrow x=8\end{array}$

The sides of the triangle are

  $\begin{array}{c}(x-5)=8-5\\ =3\end{array}$

  $\frac{x}{2}=\frac{8}{2}=4$

Thus, the sides of the triangle are 3, 4 and 6 inches.

Conclusion:

Therefore, the shortest side of the triangle is 3 inches.