Chapter 11.6, Problem 1WE

To determine

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

Answer to Problem 1WE

  $c=26$ .

Explanation of Solution

Given:

  $a=10,b=24,c=?$ .

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,

  $\begin{array}{l}{c}^2=a^2+b^2\\ ={10}^2+{24}^2\left\{\text{substitutes the given value}\right\}\\ =100+576\{\because {10}^2=100,{24}^2=576\}\\ =676\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{676}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=\sqrt{{26}^2}\{\text{simplify}}\\ c=26\{\sqrt{a^2}=a\}\end{array}$

Thus, $c=26$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=26$ .