Question

Construct a ∆ABC in which BC = 3.6 cm, AB = 5 cm and AC = 5.4 cm. Draw the perpendicular bisector of the side BC.

Answer 1

$$\begin{gathered} \begin{array}{l}\text{Steps of construction:}\\ \text{1}\text{. Draw a line segment (AB) of length 5 cm.}\\ \text{2}\text{. Draw an arc of radius 5}\text{.4 cm from the centre (A).}\\ \text{3}\text{. With B as the centre, draw another arc}\mathrm{of\; radius\; 3}\text{.6 cm, cutting the previous arc at C.}\\ \text{4}\text{. Join AC and BC}\text{.}\\ \text{5}\text{. Taking B as the centre and the radius more than half of BC, draw two arcs on both the sides of BC}\text{.}\\ \text{6}\text{. Similarly, taking C}\text{}\text{as the centre and the same radius, draw arcs on both the sides of BC, cutting the previous arcs at P and Q.}\\ \text{7. Join PQ.}\end{array} \\ \text{Then, PQ is the required perpendicuar bisector of BC, meeting BC at D.} \end{gathered}$$