Match the following columns:


Column I



Column II



A. In a given ΔABC, DE || BC and . If AC = 5.6 cm then AE = ………. cm.



P. 6



B. If ΔABC ~ ΔDEF such that 2AB = 3DE and BC = 6 cm then EF = ……….. cm.



Q. 4



C. If ΔABC ~ ΔPQR such that ar(ΔABC) : ar(ΔPQR) = 9 :16 and BC = 4.5 cm then QR = cm.



R. 3



D. In the given figure, AB || CD and OA = (2x + 4) cm, OB = (9x — 21) cm, OC = (2x —1) cm and OD = 3 cm. Then x = ?




S. 2.1




A)

Given that DE||BC,
by B.P.T.,


Let AE = x


Then, from the figure, EC = 5.6-x



5x = 3(5.6-x)


5x = 16.8-3x


8x = 16.8


x = 2.1cm


Therefore, (A)-(s)


B)
As Δ ABCΔDEF,


3EF = 2BC


3EF = 2 × 6


EF = 4cm


Therefore,(B)-(q)


C)



QR =
QR = = 6cm


Therefore (C)-(p)


D)



(BPT)



⇒ 3(2x + 4) = (2x-1)(9x-21)


⇒ 6x + 12 = 18x2-42x-9x + 21


⇒ 18x2-57x + 9 = 0


⇒18x2-54x-3x + 9 = 0


⇒ 18x(x-3)-3(x-3) = 0


⇒ (18x-3)(x-3) = 0


So, x = 3 or x =


But for x = , 2x-1<0 which is not possible.
Therefore, (D)-(r)


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