Question

Use ruler and compasses only for the following questions:
Construct triangle BCP, when CB = 5 cm, BP = 4 cm, ∠PBC = 45°.
Complete the rectangle ABCD such that :
(i) P is equidistant from AB and BC and
(ii) P is equidistant from C and D. Measure and write down the length of AB.

Answer 1

Given: BC = 5 cm, BP = 4 cm and ∠PBC = 45°
Steps of construction :
1. Constant ΔBCP with BC = 5 cm, BP = 4 cm and ∠PBC = 45°.
2. Draw perpendicular BE and CF and B and C respectively.

3. Draw perpendicular from on CF meeting CF in K.
4. Cut CD from CF, such that CK = KD.
5. Cut BA from BE, such that BA = CD.
6. Join AD.
Hence, ABCD is the required rectangle and AB = 5·7 cm.