Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.

In an isosceles triangle, median and altitude are the same.

Steps of Construction:

1. Draw base AB of side 8 cm.

2. Draw perpendicular bisector of AB.

3. Let perpendicular bisector intersect AB at point C.

4. Taking point C as center, and 4 cm radius, draw an arc intersecting perpendicular bisector at point D.

5. Join AD, and BD.

Δ ABC is the required triangle.

Now, we need to make a triangle which is its size.

Scale factor =

Steps of Construction:

1. Draw any ray AX making an acute angle with AB on the side opposite to the vertex D.

2. Mark 3 (greater of 2 and 3) points B₁, B₂, B₃ on BX so that AB₁ = B₁B₂ = B₂B₃.

3. Join B₂B and draw a line through B₃ parallel to B₂B, to intersect AB extended at B’.

4. Draw a line through B’ parallel to the line BD to intersect AD extended at D’.

Thus, Δ AB’D’ is the required triangle.