Question

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Answer 1

Steps of construction:

1. Draw a line segment $AB=7.6$ cm.

2. Draw a ray $AX$ making an acute angle at $A$ with $AB$.

3. Draw another ray $BY$ parallel to $AX$ making an acute angle.

Make sure angle must be same as considered in step 2.

4. Taking $A$ as centre draw an arc cutting at $A_1$ on the line.

Taking same radius consider $A_1$ as a centre and draw another arc cutting line at $A_2$.

Repeat the same procedure and divide the line $AX$ into $5$ points $A_1,A_2,A_3,A_4$.and $A_5$

In such a way, $A{A}_1=A_1{A}_2=A_2{A}_3=A_3{A}_4$

5. Similar to step $4$,

Taking $B$ as centre draw an arc cutting at $B_1$ on the line.

Taking same radius (set in step 4) consider $B_1$ as a centre and draw another arc cutting arc cutting line at $B_2$.

Repeat the same procedure and divide the line $BY$ into $8$ points in such a way that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4=B_4{B}_5=B_5{B}_6=B_6{B}_7=B_7{B}_8$

6. Join $A_5{B}_8$

7. Line $A_5{B}_8$ intersect $AB$ at a point $P$ in the ratio $5:8$

8. Measurement : $PB=4.7$ cm and $AP=2.9$ cm