Question

Construct a ΔABC, right-angled at B with a perimeter of 10 cm and one acute angle of 60°.

Answer 1

Steps of construction:
1. Draw DE = 10 cm.
2. Draw DP and EQ such that ∠PDE = 90° and ∠QED = 60°.
3. Draw AD and AE, the bisectors of angles PDE and QED respectively, intersecting each other at A.
4. Draw perpendicular bisector of AD and AE, interesting DE at points B and C respectively.
5. Join AB and AC.
Thus, ABC is the required triangle.