Chapter 14, Problem 11RP

To determine

To construct an equilateral triangle with the perimeter equal to segment’s length.

Answer to Problem 11RP

Draw the equilateral triangle of side length of $\frac{a}{3}$ where $a$ is the length of the line segment.

Explanation of Solution

Given:

The perimeter of equilateral triangle is equal to segment’s length.

Calculation:

The following is the required equilateral triangle-

  

Step 1- Draw the first side AB with the length of $\frac{a}{3}$ where $a$ is the length of the line segment.

Step 2- Draw two angles of ${60}^{\circ }$ at both end points.

Step 3- Extend the ${60}^{\circ }$ angle lines to get the point C.

Step 4 − The triangle ABC is the required equilateral triangle.