Question

Construct an isosceles triangle whose base is 7.5 cm and altitude 3.5 cm then another triangle whose sides are 4/7 times the corresponding sides of the isosceles triangle.

Answer 1

Steps of construction :

1. Draw a line BC =  7.5 cm.

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

3. Cut the line OA = 3.5 cm.

4. Join A to B and, A to C.

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

6. Locate 7 points at equal distance among B₁,B₂,............, B₇ on line segment BX.

7. Join B₇C. Draw a parallel line through B₄ to B₇C intersecting line segment BC at C'.

8. Through C' draw a line parallel to AC intersecting line segment AB at A'.

9. Hence, ΔA'BC' is a required triangle