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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 $$AP=2.9$$ cm

1537923_1063371_ans_9c40d345812248d4a3d5c90a02fa5775.png

Mathematics
RS Agarwal
Standard X

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