divide a line segment ab=8cm in the ratio 2:3:4 - Maths - Constructions

Question

divide a line segment ab=8cm in the ratio 2:3:4

Ankush Jain · Accepted Answer

To divide a line segment of length 8 cm in the ratio 2:3:4, we
follow the below given steps

We draw a line segment PQ of length 8 cm

Now, we draw a ray PX making an acute angle with PQ and draw a ray
QY parallel to PX by making âˆ PQY equal to
âˆ QPX

Firstly, we locate 5 points P1,
P2,
P3,
P4,
and P5
on PX and 4 points Q1,
Q2,
Q3
and Q4
on QY such that PP1
= P1P2
= P2P3
= P3P4=
P4P5
= QQ1
= Q1Q2
= Q2Q3=
Q3Q4

Now, we join P5Q4
which intersects PQ at S Therefore, PS : SQ = 5 : 4

Now, we divide PS in the ratio 2 : 3 by again repeating the same
procedure

6 Now, we draw a ray SZ parallel to PX by making
âˆ PSZ equal to âˆ QPX

7 Firstly, we locate 2 points P1
and P2
on PX and 3 points x1,
x2
and x3
on SZ such that PP1
= P1P2
= Sx1
= x1x2=
x2x3

8 Now, we join P2x3
which intersects PS at R Therefore, PR : RS = 2 : 3

Hence, PR : RS : SQ = 2 : 3 : 4

Hope you get it!!