Question

Draw ΔABC with AB = 4 cm, BC = 5 cm and CA = 6 cm. Draw an isosceles triangle of the same area with one side as AB itself.

Answer 1

The dimensions of the triangle to be constructed are AB = 4 cm, BC = 5 cm and CA = 6 cm.

The steps of construction are as follows:

1) Draw a line segment AB of length 4 cm.

2) Taking A as the centre and 6 cm as the radius, draw an arc on the upper side of line segment AB.

3) Taking B as the centre and 5 cm as the radius, draw an arc cutting the previously drawn arc at point C.

4) Join AC and BC.

ΔABC is the required triangle.

We know that triangles lying on the same base and between the same parallels are equal in area.

We also know that any point lying on the perpendicular bisector of a line segment is equidistant from the end points of that line segment.

Here, we need to draw an isosceles triangle whose base is AB and whose area is equal to the area of ΔABC.

So, we will use both these properties to construct the required triangle.

The steps of construction are as follows:

1) Draw a line l that is parallel to line segment AB and passes through point C.

2) Draw the perpendicular bisector of line segment AB by taking A and B as the centres. Draw arcs of radius more than half the length of AB. Let the perpendicular bisector intersect line l at point D.

3) Join AD and BD.

ΔABD is the required isosceles triangle with DA equal to DB and area of ΔABC equal to area of ΔABD.