Chapter 10.8, Problem 13WE

To determine

To construct: $\Delta ABC$ so that $AB=t$ , and the median to $\overline{AB}$ and the altitude to $\overline{AB}$ have lengths $s$ and $r$ , respectively.

Explanation of Solution

Given Information:

Use figure,

  

Calculation:

Draw $AB=t$ .

Construct perpendicular bisector of line $\overline{AB}$ .

  $X$ is the midpoint of $\overline{AB}$ .

Cut an arc of length $r$ from $X$ .

Construct a perpendicular at distance $r$ , draw line $m$ parallel to $\overline{AB}$ .

Cut an arc of length $s$ from midpoint $X$ on line $m$ .

Join $C,A,$ and $C,B$ .

Here, $\Delta ABC$ is required triangle where median $CX=s$ .

The figure is shown below: