Chapter 10, Problem 26CR

To determine

To construct: the isosceles triangle with hypotenuse of length a.

Explanation of Solution

Given information:

The given line segments are as follows:

  

The given line segments are of length given below.

  $\begin{array}{l}b=2cm,\\ c=1cm\\ t^2=bc=\sqrt{2}\end{array}$

Procedure to construct the line t:

• Draw the line $AB$.
• From A draw the arcs on either side of it intersecting the line.
• as two intersecting points as centers with the any radius draw two arcs.
• Draw the line joining the intersecting point and the point A.
• from point B, with the length a, draw an arc intersecting at C.
• Draw the line $AC$
• Then required triangle $ABC$ is formed.

The line segment t is shown below.

  

Hence, the isosceles triangle with hypotenuse of length a is construced.