Chapter 8, Problem 18CT

To determine

To find: the value of x

Answer to Problem 18CT

The value of x is 6

Explanation of Solution

Given Information: A triangle with a right angle and a perpendicular directed to the hypotenuse.

Formula used:

For a right triangle NDF with a perpendicular NE being drawn to the hypotenuse DF (as shown below), the relation between NE and the hypotenuse is expressed as,

  

  $\begin{array}{l}N{E}^2=DE\times EF\\ NE=\sqrt{DE\times EF}\end{array}$.......(1)

Calculation:

Consider the right triangle given below.

  

Here, applying the relation in (1), the value of x can be obtained as,

  $\begin{array}{c}2\sqrt{6}=\sqrt{4\times x}\\ =2\sqrt{x}\\ x=6\end{array}$