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  • In each of the following, give the justification of the construction also:. Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

In each of the following, give the justification of the construction also:
1. Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

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Steps of construction:-

(i) Draw a line segment AB of measurement 7.6 cm (length).

(ii) Now draw an acute angle AC with line segment AB.

(iii) Now cut 13 equal points on the line AC where the zeroth point is A.

(iv) Join the 13th point with point B. So the new line is BA13.

(v) Now, from point A5 draw a line parallel to BA13 on line AB. Name the point as D.

The point D is the required point which divides the line segment in the ratio of 5: 8.

The length of the two parts obtained are 2.9 cm and 4.7 cm for AD and DB respectively.

 

                                                                               Constructions, 24670

Justification:-   In the figure, we can see two similar triangles:\Delta ADA_5 and       \Delta ABA_{13}

                          Thus                  \frac{AA_5}{A_5A_{13}}\ =\ \frac{AD}{DB}\ =\ \frac{5}{8}.

 

Posted by

Devendra Khairwa

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