A line segment of length 7.6 cm can be divided in the ratio of 5:8 as follows. Step 1 Draw line segment AB of 7.6 cm and draw a ray AX making an acute angle with line segment AB. Step 2 Locate 13 (= 5 + 8) points, A1, A2, A3, A4 …….. A13, on AX such that AA1 = A1A2 = A2A3 and so on. Step 3 Join BA13. Step 4 Through the point A5, draw a line parallel to BA13 (by making an angle equal to ∠AA13B) at A5intersecting AB at point C. C is the point dividing line segment AB of 7.6 cm in the required ratio of 5:8. The lengths of AC and CB can be measured. It comes out to 2.9 cm and 4.7 cm respectively. Justification The construction can be justified by proving that `(AC)/(CB) = 5/8` By construction, we have A5C || A13B. By applying Basic proportionality theorem for the triangle AA13B, we obtain `(AC)/(CB) =(` 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 `(AC)/(CB) = 5/8` This justifies the construction Open in App Suggest Corrections 16 Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesPage 2Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all courses |