Chapter 8, Problem 6CT

To determine

To fill the blanks: with the appropriate measure of the side of the triangle mentioned for a given figure

Answer to Problem 6CT

The measure of ND is $5\sqrt{10}$

Explanation of Solution

Given Information: A triangle DNF with a right angle and a perpendicular directed to the hypotenuse. The measure of sides DE and EF are 10 and 15 respectively

Formula used :

For a right triangle DNF with a perpendicular NE being drawn to the hypotenuse DF (as shown below), the relation between the one of the legs of the bigger triangle and the normal to it is expressed as,

  

  $\begin{array}{l}N{D}^2=DE\times DF\\ ND=\sqrt{DE\times DF}\end{array}$

Calculation: Consider the following figure. Here, the sides DE and DF are given as

DE=10

  $\begin{array}{c} DF=DE+EF\\ =10+15\\ =25\end{array}$

  

Substituting the measure of DE and DF in the above formula , the measure of side ND can be obtained as,

  $\begin{array}{c}ND=\sqrt{10\times 25}\\ =5\sqrt{10}\end{array}$