Draw a line segment of length 7.6c.m and divides in it the ratio 5:8 measure the two parts

Draw a line segment of length 7.6c.m and divides in it the ratio 5:8 m

1.	Draw a line segment of length 7.6c.m and divides in it the ratio 5:8 measure the two parts
Answer» Given: A line segment of length 7.6 cm.Required: To divide it in the ratio 5 : 8 and to measure the two parts.Steps of construction :\tFrom any ray AX, making an acute angle with AB.\tLocate 13 (= 5 + 8) points A1,\xa0A2, A3,..... and A13\xa0on AX such that\tAA1\xa0= A1A2\xa0= A2A3\xa0= A3A4\xa0=\xa0A4A5\xa0= A5A6\xa0= A6A7\xa0= A7A8\xa0= A8A9\xa0= A9A10\xa0= A10A11\xa0= A11A12\xa0= A12A13\tJoin BA13\tThrough the point A5, draw a line parallel to A13B intersecting AB at the point C.\tThen, AC : CB = 5 : 8\tOn measurement, AC = 3.1 cm, CB = 4.5 cm.Justification :{tex}\\because{/tex}\xa0A5C \|\| A13B [ By Construction]{tex}\\because{/tex}\xa0{tex}\\frac { A A _ { 5 } } { A _ { 5 } A _ { 13 } } = \\frac { A C } { C B }{/tex}\xa0[By the Basic proportionality theorem]But,\xa0{tex}\\frac { A A _ { 5 } } { A _ { 5 } A _ { 13 } } = \\frac { 5 } { 8 }{/tex}\xa0[ By Construction[Therefore,\xa0{tex}\\frac { A C } { C B } = \\frac { 5 } { 8 }{/tex}This shows that C divides AB in the ratio 5 : 8.