Chapter 10.5, Problem 8WE

To determine

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

Explanation of Solution

Given Information:

Given condition,

  $3x=w+2y$

Given figure,

  

Calculation:

Construct a segment $x$ such that following condition holds true:

  $3x=w+2y$

Draw $\overline{AL}=w$ and $\overline{LB}=2y$ such that $\overline{AB}=w+2y$

Trisect $\overline{AB}$ as follows,

Choose any point $Z$ not on $\overline{AB}$ and draw $\overline{AZ}$ .

Take any radius mark off $R$ on $\overline{AZ}$ taking $A$ as center, now take $R$ as center and mark off $S$ on $\overline{AZ}$ and again take $S$ as center off $T$ on $\overline{AZ}$ .

Since, $AR=RS=ST$

Draw $\overline{TB}$

At $R$ and $S$ draw lines parallel to $\overline{TB}$ intersecting $\overline{AB}$ at $X$ and $Y$ .

Further, $\overline{AB}$ is divided into three equals parts $AX=XY=YB=x$ and hence, $3x=w+2y$ .