Chapter 11.6, Problem 21WE

To determine

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

Answer to Problem 21WE

  $c=16.970$ .

Explanation of Solution

Given:

  $a=b=12,c=?$ .

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,

  $\begin{array}{l}{c}^2=a^2+b^2\\ ={12}^2+{12}^2\left\{\text{substitutes the given value}\right\}\\ =144+144\{\because {12}^2=144\}\\ =288\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{288}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=16.970\{\text{up to nearest hundred}}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=16.970$ .