Chapter 11.6, Problem 24WE

To determine

To find: the missing length correct to the nearest hundred in the given triangle.

Answer to Problem 24WE

  $c=15.491$ .

Explanation of Solution

Given:

  $a=\frac{1}{2}b,b=14,c=?$ .

The given triangle is shown below:

  

Calculation:

As the given triangle is right angle tringle.

Therefore, by using Pythagoras theorem, $c^2=a^2+b^2$

Thus,

  $\begin{array}{l}{c}^2=a^2+b^2\\ ={18}^2+3^2\{b=14,a=\frac{14}{2}=7\}\\ =196+49\{\because {14}^2=196,7^2=49\}\\ =245\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{240}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=15.491\{\text{up to nearest hundred}}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=15.491$ .