Question

Draw ΔABC as in the first problem. Draw a triangle of the same area with two of its sides 6 centimetres and 7 centimetres.

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.

Here, we need to construct a triangle whose base is BC of length 6 cm and one other side of length 7 cm. The area of this triangle should be equal to the area of ΔABC.

The steps of construction are as follows:

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

2) Taking B as the centre and 7 cm as the radius, draw an arc which intersects line l at a point, say D.

3) Join BD and CD.

ΔBCD is the required triangle with BC = 6 cm and BD = 7 cm and area of ΔABC equal to the area of ΔADC.