Divide a given line segment in ratio of 3 : 5 and write steps of construction.

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Solution

Let AB be our given line segment.
To construct:
Divide AB in the ratio of 3 : 5.
Steps of construction
1) Draw $¯ ¯¯¯¯¯¯ ¯ A B$ .
2) Draw $- - \to A X$ , making an acute angle with AB.
3) Locate 8(= 3 + 5) points $A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}, A_{7}$ and $A_{8}$ on $- - \to A X$
so that $A A_{1} = A_{1} A_{2} = A_{2} A_{3} = A_{3} A_{4} = A_{4} A_{5} = A_{5} A_{6} = A_{6} A_{7} = A_{7} A_{8}$ .
4) Join $B A_{8}$ .
5) Through the point $A_{3}$ draw a line parallel to $A_{8} B$
(By making an angle equal to $∠ A A_{8} B$ ) at $A_{3}$ intersecting AB at the point C.
Then AC : CB = 3 : 5.

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