Construct an isosceles triangle whose base is 6 𝑐𝑚 and altitude 4 𝑐𝑚. Then construct another triangle with sides that are $\frac{3}{4}$ times the corresponding sides of the isosceles triangle.

We need to construct an isosceles triangle with base 6 𝑐𝑚 and altitude 4 𝑐𝑚 and another triangle with sides that are $\frac{3}{4}$ times the corresponding sides of the isosceles triangle.

Steps of construction: 

1. Draw a line segment BC = 6 cm. 

2. Draw a perpendicular bisector of BC which intersects the line BC at Q. 

3. Mark A on the line such that OA = 4 cm. 

4. Join A to B and C. 

5. Draw a ray BX making an acute angle with BC. 

6. Mark four points B1 , B2 , B3 , and B4 on the ray BX; such that BB1 = B1B2 = B2B3 = B3B4 . 

7. Join B4C. 8. Draw a line parallel to B4C through B3 intersecting line segment AB at A'. Hence ΔA'BC' is the required triangle.