Construct a triangle which is similar to a triangle whose sides are AB=5cm BC=8cm and angle B=40 in the ratio 5 upon 7

The steps of construction are as follows:

1. First Draw the triangle ABC as per given.

2. Draw a ray BX making an acute angle with BC on opposite side of vertex A.

3. Locate 7 points (as 7 is greater in 5 and 7). B₁, B₂, B₃, B₄ ,B₅, B₆, B₇ on line segment BX.

 4. Join B₇C and draw a line through B₅, parallel to B₇C intersecting BC at C'.

5. Draw a line through C' parallel to AC intersecting AB at A'. DA'BC' is the required triangle.