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Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts Q.1

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How i draw a line segment type question form class 10th ncert book of class 10th of chapter constructions of exercise 11.1, give me the best and easy way to draw this question Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts


1 Answer

  1. Construction Procedure:

    A line segment with a measure of 7.6 cm length is divided in the ratio of 5:8 as follows.

    1. Draw line segment AB with the length measure of 7.6 cm

    2. Draw a ray AX that makes an acute angle with line segment AB.

    3. Locate the points i.e.,13 (= 5+8) points, such as A1, A2, A3, A4 …….. A13, on the ray AX such that it becomes AA1 = A1A2 = A2A3 and so on.

    4. Join the line segment and the ray, BA13.

    5. Through the point A5, draw a line parallel to BA13 which makes an angle equal to ∠AA13B

    6. The point A5 which intersects the line AB at point C.

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

    8. Now, measure the lengths of the line AC and CB. It comes out to the measure of 2.9 cm and 4.7 cm respectively.

    Ncert solutions class 10 Chapter 11-1


    The construction of the given problem can be justified by proving that

    AC/CB = 5/ 8

    By construction, we have A5C || A13B. From Basic proportionality theorem for the triangle AA13B, we get

    AC/CB =AA5/A5A13….. (1)

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

    Therefore, it becomes

    AA5/A5A13=5/8… (2)

    Compare the equations (1) and (2), we obtain

    AC/CB = 5/ 8

    Hence, Justified.

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