Chapter 11.6, Problem 22WE

To determine

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

Answer to Problem 22WE

  $c=15.297$ .

Explanation of Solution

Given:

  $a=15,b=\frac{1}{5}a,c=?$ .

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,

  $\begin{array}{l}{c}^2=a^2+b^2\\ ={15}^2+3^2\{a=15,b=\frac{15}{5}=3\}\\ =225+9\{\because {15}^2=225,3^2=9\}\\ =234\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{234}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=15.297\{\text{up to nearest hundred}}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=15.297$ .