Question

To construct a triangle, with perimeter 10 cm and base angles 60° and 45°.

Answer 1

Given: In ∆ABC
AB + BC + CA = 10 cm, ∠B = 60° and ∠C = 45°.
Required: To construct ∆ABC.

Steps of Construction :
1. Draw DE = 10 cm
2. At D, construct ∠EDP = $\frac{1}{2}$ of 60°= 30° and at E, construct ∠DEQ =$\frac{1}{2}$ of 45° = 22 ${\frac{1}{2}}^{\circ }$
3. Let DP and EQ meet at A.
4. Draw perpendicular bisector of AD to meet DE at B.
5. Draw perpendicular bisector of AE to meet DE at C.
6. Join AB and AC. Thus, ABC is the required triangle.