Chapter 14, Problem 7CTE

To determine

To find: the value of $\sqrt{xy}$ with $x>y$ , where $x,y$ are two line segment.

Answer to Problem 7CTE

  $\sqrt{xy}=9.52$

Explanation of Solution

Given information:

Instructed to draw two lines $x,y$ with $x>y$ . So suppose $AB,CD$ are two lines so that $AB(=y)<CD(=x)$ .

  

Calculation:

To find , we can rewrite it as, $\sqrt{xy}=\sqrt{x}\times \sqrt{y}$ .

Now for $\sqrt{y}=\sqrt{AB}$ , consider the following figure,

  

Where we extend $AB$ to $G$ and draw a semicircle with diameter $GB$ . Now making a perpendicular on $A$ which meet the semicircle at $H$ . Therefore the distance $AH=\sqrt{AB}=\sqrt{y}=\sqrt{8}=2.8$ .

Similarly for the segment $x=CD$ , to find $\sqrt{x}=\sqrt{CD}$ , considering the following figure,

  

Where we extend $CD$ to $E$ and draw a semicircle with diameter $ED$ . Now making a perpendicular on $C$ which meet the semicircle at $F$ . Therefore the distance $CF=\sqrt{CD}=\sqrt{x}=\sqrt{12}=3.4$ .

Hence,

  $\sqrt{xy}=\sqrt{x}\times \sqrt{y}=2.8\times 3.4=9.52$