Q. 14.1( 352 Votes )

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

Answer :

Step 1: Draw line segment AB = 7.6 cm



Step 2: Draw a ray AC making an acute angle with line segment AB .



Step 3: Along AC, divide (5+8) 13 equals points


A1,A2,A3,……………….,A13 on AX such that


AA1=AA2=A2A3 and so on .



Step 4: Join BA13



Step 5: Through the point A5, draw a line parallel to BA13 (by making an angle equal to AA13B) at A5 intersecting AB at point D.


C is the point dividing line segment AB of 7.6 cm in the required ratio of 5:8.


The lengths of AD and DB can be measured. It comes out to 2.9 cm and 4.7 cm respectively.



Justification


The construction can be justified by proving that



By construction, we have A5DA13B. By applying Basic proportionality theorem for



From the figure, it can be observed that AA5 and A5A13 contain 5 and 8 equal divisions of line segments respectively.



On comparing equations (1) and (2), we obtain



This justifies the construction.

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