Chapter 10.8, Problem 16WE

To determine

To construct: a square whose sides have lengths $4s$ by using the given segments.

Answer to Problem 16WE

Side of the square $=14.2$ centimeters

Explanation of Solution

Given:

An angle and 3 line segments.

  

Given condition: Side of the square $=4s$ .

Calculation:

Draw the segments roughly as long as those given.

  

Measure the drawn segments,

  $r=3.02$ centimeters

  $s=3.55$ centimeters

  $t=5.03$ centimeters

Now,

Side of the square $=4s=4\times 3.55$

  $\Rightarrow$ side of square $=14.2$ centimeters.

  

Now let us move the $3s$ segment.

So the locus of the midpoint of line segment with measure as $3s$ .

  

So the locus of the midpoint of line segment with measure as $3s$ .

  

The locus of the midpoint of line segment $3s$ is the perpendicular bisector of the segment.

Conclusion:

Hence, the side of the square is 14.2 centimeters.

The locus of midpoint of line segment is $3s$ the perpendicular bisector of the segment.