#### Question

Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.

#### Solution

Steps for construction:

1. Draw a line segment AB = 5 cm.

2. At B construct m∠ABC = 60°

3. Take a measure of 6 cm, and draw an arc from B on BC.

4. Join AC to obtain ΔABC.

5. Below AB, make an acute angle ∠BAX.

6. Since 7 > 5, mark off 7 points A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6} and A_{7} such that AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} = A_{4}A_{5} = A_{5}A_{6} = A_{6}A_{7}.

7. Join A_{7}B.

8. Since we have to construct a triangle each of whose sides is 5/7 of the corresponding sides of ABC. So take five parts out of seven equal parts on AX. i.e. from point A5, draw A5B' || A7B, meeting AB at B'.

9. From B', draw B'C' || BC, meeting AC at C'

10.ΔAB'C' is the required, each of the sides is five-seventh of the corresponding sides of ΔABC.