Question

Construct a triangle ABC in which BC is 3.5 cm, angle B is ${75}^{\circ }$ and AB + AC = 6.5 cm.

Answer 1

Steps:
1. Draw line segment BC of length 3.5 cm using ruler.
At B, construct an angle of measure ${75}^{\circ }$. Draw a ray BX.
2. Cut a line segment BD equal to AB + AC = 6.5 cm on ray BX.
3. Join CD.
4. Draw the perpendicular bisector of CD, intersecting BD at point A.
5. Join AC.
6. ABC is the required triangle.