Chapter 8, Problem 4CR

To determine

To find: the value of z.

Answer to Problem 4CR

The value of z is $5\sqrt{3}$

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 both small triangles are congruent to each other and to the bigger triangle.

  

This gives the relation,$\begin{array}{l}{a}^2=cy\\ a=\sqrt{cy}\end{array}$

Calculation:

Consider the triangle shown below.

  

For the given triangle, the one of the legs of the bigger triangle is represented by z and the parts of the hypotenuse considered is 5 and the total length of hypotenuse being 15. Thus, comparing with the general figure and formula, the value of z can be calculated as,

  $\begin{array}{c}z=\sqrt{5\times 15}\\ =\sqrt{75}\\ =5\sqrt{3}\end{array}$