Chapter 10.5, Problem 13WE

To determine

To calculate: Construct a segment of length $x=\sqrt{6yz}$.

Answer to Problem 13WE

  

Explanation of Solution

Given information:

  $x=\sqrt{6yz}$

Calculation:

  $x=\sqrt{6yz}$ is a geometric mean of $3y$ and $2z$ ( from many other possibilities) Now, draw segment $3y$ and $2z$ by tripling and doubling y and z respectively, Then,

Geometric mean can be drawn by,

Step 1: Draw two numbers in one line as shown in figure

Step 2: From the midpoint draw a semicircle by taking any other end point as end of radius.

Step 3: Draw a perpendicular from the intersecting point of two numbers. Which is the required geometric mean line.