Question

Draw ΔABC, with AB = 5 cm and BC = 7 cm and ∠ABC = 60°. Draw a triangle of the same area with one side as AB and the angle at B equal to 30°

Answer 1

The measures of the sides and the angle of the triangle to be constructed are AB = 5 cm, BC = 7 cm and ∠ABC = 60°.

The steps of construction are as follows:

1) Draw a line segment BC of length 7 cm.

2) Draw ∠XBC of measure 60° at point B.

3) Taking B as the centre and 5 cm as the radius, draw an arc which intersects ray BX at point A.

4) Join AC.

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 one side AB = 5 cm, angle at B = 30° and whose area is equal to the area of ΔABC.

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 ∠DBC of measure 30° such that point D is lying on line l.

3) Join AD.

ΔABD is the required triangle whose one side AB = 5 cm, angle at B = 30° and area of ΔABC is equal to the area of ΔABD.