Chapter 10.5, Problem 11WE

To determine

To construct a segment that has length $x$ satisfying the given condition.

Answer to Problem 11WE

  $x=2.3$ centimeters

Explanation of Solution

Given:

Four line segments

  

Given condition: $x=\frac{1}{3}\sqrt{yp}$

Calculation:

Draw the four segments roughly as long as those given.

  

Measure the segments drawn,

  $w=4.8$ centimeters

  $y=3.44$ centimeters

  $z=6.99$ centimeters

  $p=13.86$ centimeters

Now,

  $x=\frac{1}{3}\sqrt{yp}$ (given)

Putting the values,

  $\Rightarrow x=\frac{1}{3}\sqrt{(3.44)(13.86)}$

  $\Rightarrow x=2.3$

Therefore, $x=2.3$ centimeters

Now draw a line segment of length 10.03 centimeters.

  

Conclusion:

Therefore, the line segment $x$ is of length 2.3 centimeters.