Question

draw a line segment of length 7.6cm and divide in ratio 5:8 measure the two parts.give the justification of construction

Answer 1

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Answer 2

Given: Length of line segment 7.6 cm and ratio 5 : 8 i.e., m : n.

Step-by-step Construction:

Step 1: Draw a line segment AB of length 7.6 cm.

Step 2: Draw any ray AX, making an acute angle with AB.

Step 3: Locate 13 ( = m + n ) points $A_1\,,\,A_2\,,\,A_3\,,\,A_4\,,\,A_5\,,\,A_6\,,\,A_7\,,\,A_8\,,\,A_9\,,\,A_{10}\,,\,A_{11}\,,\,A_{12}\,,\,A_{13}$ on AX so that $AA_1=A_1A_2=A_2A_3=A_3A_4=A_4A_5=A_5A_6=A_6A_7=A_7A_8=A_8A_9=A_9A_{10}=A_{10}A_{11}=A_{11}A_{12}=A_{12}A_{13}$

Step 4: Join $BA_{13}$

Step 5: Through the point $A_5$ ( m = 5 ) , draw a line parallel to $A_{13}B$ ( by making an angle equal to $\angle AA_{13}B$ )  at $A_5$ intersecting AB at the point C.

So, we get

⇒ AC : CB = 5 : 8

⇒ AC = 2.9 cm  and CB = 4.7 cm

Figure is attached