Question

Draw triangle of sides 6, 7 and 8 centimetres. Divide it into three triangles whose areas are in the ratio 1 : 2 : 3.

Answer 1

The dimensions of the required triangle are AB = 6 cm, CA = 7 cm and BC = 8 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 7 cm as the radius, draw an arc on the upper side of AB.

3) With B as the centre and 8 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 need to divide the given triangle into three triangles whose areas are in the ratio 1 : 2 : 3.

Height of all the triangles so formed would be equal to the height of the original triangle.

Let the first triangle be ΔADC.

Area of ΔADC = × Area of ΔABC

× Area of ΔABC

Let the second triangle be ΔDEC.

Area of ΔDEC = × Area of ΔABC

× Area of ΔABC

ΔEBC so formed, after the construction of the above two triangles, has area equal to half the area of ΔABC.

The steps of construction are as follows:

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

2) Join CD.

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

4) Join CE.

Thus, ΔADC, ΔDEC and ΔEBC are the required triangles whose areas are in the ratio 1 : 2 : 3.