Q. 15.0( 1 Vote )

In ΔABC, a line parallel to intersects and in D and E respectively. Fill in the blanks shown in the table :


Answer :

Given, In ΔABC, a line parallel to intersects and in D and E respectively as shown in fig.


In ABC, a line parallel to BC intersects AB and AC in D and E respectively.


...... (i)


...... (ii)


…… (iii)


Also, AB = AD + DB and AC = AE + EC


1) AB = AD + DB


AB = 3.6 + 2.4


AB = 6


Now from eq (i)




AE =


AE = 2.7


But, AC = AE + EC


AC = 2.7 + 1.8 = 4.5


AC = 4.5


2) AC = AE + EC


4.2 = AE + 3.15


AE = 1.05


From eq (ii)




AD =


AD = 1.55


Then AB = AD + DB


6.2 = 1.55 + DB


DB = 4.65


3) AC = AE + EC


AC = 6.4 + 8.0


AC = 14.4


From eq (i)



AD =


AD = 9.6


AB = AD + DB


AB = 9.6 + 12


AB = 21.6


4) From eq (ii)




AC =


AC = 13.8


AB = AD + DB


18.4 = 7.2 + DB


DB = 18.4 – 7.2


DB = 11.2


Then, AC = AE + EC


13.8 = 5.4 + EC


EC = 8.4


5) From eq (iii)




AB =


AB = 6.8


AB = AD + DB


6.8 = AD + 3.4


AD = 3.4


AC = AE + EC


5.1 = AE + 2.55


AE = 2.55



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