Chapter 12.5, Problem 1CK

To determine

Toprove:The length of the side VOis equal to $4$ with the help of Pythagoras theorem.

Explanation of Solution

Given information:

The figure is shown below:

  

Proof:

According to the Pythagoras theorem in a right angle triangle, the sum of squares of its base and perpendicular is equal to the square of its hypotenuse.

It is given that $\Delta VOB$ is right angledVO is perpendicular, VB is hypotenuse and OB is base. So,

  $\begin{array}{c}V{O}^2+O{B}^2=V{B}^2\\ V{O}^2+3^2=5^2\\ V{O}^2+9=25\end{array}$

Further simplify.

  $\begin{array}{c}V{O}^2=16\\ VO=\sqrt{16}\\ VO=4\end{array}$

Hence, by the Pythagoras theorem it is proved that the length of the side VO is $4$ .