Question

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

Solution

## 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, $$AA_1=A_1A_2=A_2A_3=A_3A_4$$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 $$BB_1=B_1B_2=B_2B_3=B_3B_4=B_4B_5=B_5B_6=B_6B_7=B_7B_8$$6. Join $$A_5B_8$$7. Line $$A_5B_8$$ intersect $$AB$$ at a point $$P$$ in the ratio $$5:8$$8. Measurement :  $$PB=4.7$$ cm and $$AP=2.9$$ cmMathematicsRS AgarwalStandard X

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