Chapter 8, Problem 2CR

To determine

To find: the value of x.

Answer to Problem 2CR

The value of x is $5\sqrt{2}$

Explanation of Solution

Given Information: A triangle with a right angle and a perpendicular directed to the hypotenuse. The measure of sides is marked.

Formula used:

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

  

  $\begin{array}{l}{h}^2=xy\\ h=\sqrt{xy}\end{array}$

This implies the length of the normal is the geometric mean of the two parts of the hypotenuse divided by it.

Calculation :

Consider the triangle shown below.

  

For the given triangle, the altitude is represented by x and the parts of the hypotenuse are 10 and 5. Thus, comparing with the general figure and formula, the value of x can be calculated as,

  $\begin{array}{c}x=\sqrt{10\times 5}\\ =\sqrt{50}\\ =5\sqrt{2}\end{array}$