Construct an isosceles triangle whose base is 9 cm and altitude 5 cm. Construct another triangle whose sides are of the corresponding sides of the first isosceles triangle.

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

Steps of Construction:

1. Draw a line segment CD = 9 cm.

2. Draw perpendicular bisector of CD. Let the point at which perpendicular bisector intersects CD be E.

3. Draw an arc of length 5 cm from E on the perpendicular bisector. Let the point be P.

4. Join CP and DP.

5. Δ PCD is the required isosceles triangle.

Now, we have to construct another triangle whose sides are times the corresponding sides of the isosceles triangle.

Steps:

1. Draw a ray CX on the side opposite to the vertex E such that ∠ DCX is acute.

2. Mark 4 points D₁, D₂, D₃, D₄ on CX such that CD₁ = D₁D₂ = D₂D₃ = D₃D₄.

3. Join D₄D.

4. Draw D₃D’ parallel to D₄D such that D’ lies on CD.

5. Draw D’E’ parallel to DE such that E’ lies on CE.

Δ CE’D’ is the triangle whose sides are times the corresponding sides of the isosceles triangle.