Question

Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.

Answer 1

Given:

BC = 6 cm, AC = 8 cm

The triangle to be formed is to be right angled triangle.

Steps of construction:

1. Draw a line segment BC = 6 cm.

2. Draw a ray CN making an angle of 90° at C.

3. With C as centre, taking 8 cm as the radius make an arc at CN intersecting it at A. Join AB.

4. Now, ABC is the triangle whose similar triangle is to be drawn.

5. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

6. Locate 5 (Greater of 3 and 5 in `3/5` ) points B₁, B₂, B₃, B₄ and B₅ on BX so that BB₁= B₁B₂ = B₂B₃= B₃B₄ = B₄B₅

7. Join B₅C and draw a line through B₃ (Smaller of 3 and 5 in `3/5` ) parallel to B₅C to intersect BC at C’.

8. Draw a line through C’parallel to the line CA to intersect BA at A’.

9. A’BC’ is the required similar triangle whose sides are `3/5` times the corresponding sides of ΔABC.