Question

Draw a triangle of sides 4, 5 and 6 centimetres. Divide it into two triangles, one with one-third the area, and the other with two-thirds the area, of the original triangle.

Answer 1

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

The steps of construction are as follows:

1) Draw a line segment AB of length 6 cm.

2) With A as the centre and 4 cm as the radius, draw an arc on the upper side of AB.

3) With B as the centre and 6 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.

Let the triangle with area equal to one-third of the area of ΔABC be ΔADC.

Height of both the triangles would be same.

Thus, we need to construct ΔADC such that AD = 2 cm.

The steps of construction are as follows:

1) With A as the centre and 2 cm as the radius, draw an arc on AB and name it as D.

2) Join DC.

ΔADC so obtained has area equal to one-third the area of ΔABC and ΔDBC has area equal to two-third of the area of ΔABC.