Chapter 10.5, Problem 16WE

a.

To determine

To calculate: $x$ is a geometric mean between $a$ and ___.

Answer to Problem 16WE

  $an$

Explanation of Solution

Given information:

  $x=a\sqrt{n}$

Calculation:

Geometric mean of two numbers/variables is a square root of multiplication of two numbers,

Now, the geometric mean of two numbers are given, which is $x=a\sqrt{n}$ ,

Now, $x=\sqrt{N_1{N}_2}$ , where, $N_1=a$

  $\therefore a\sqrt{n}=\sqrt{a{N}_2}$

  $\therefore N_2=an$

b.

To determine

To calculate:Construct a segment of length $a\sqrt{n}$ for $n=2,3,4$ , $a=3$ cm.

Answer to Problem 16WE

  

Explanation of Solution

Given information:

  $x=a\sqrt{n}$

Calculation:

From the (a), Geometric mean of $a$ and $an$ is $a\sqrt{n}$

By using these,

For, $n=2$ Geometric mean of 3 and 6 is $3\sqrt{2}$

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.

  

For, $n=3$ Geometric mean of 3 and 9 is $3\sqrt{3}$

  

For, $n=4$ Geometric mean of 3 and 12 is 6