Chapter 10.8, Problem 14WE

To determine

To construct: a right triangle such that the altitude to the hypotenuse and the median to the hypotenuse have lengths $r$ and $s$ , respectively.

Explanation of Solution

Given Information:

Use figure,

  

Calculation:

Draw a line $\overline{BC}$ of suitable length.

Construct perpendicular bisector of the line $\overline{BC}$ . $X$ is the midpoint of $\overline{BC}$ .

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

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

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

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

Here $\Delta ABC$ is the required triangle where median $AX=s$ .

The figure is shown below: