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In the given figure $D E | | A C, D F | | A E$ . If the lengths of BF and FE in cm are 4 and 5 respectively, then find the length of EC.

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12.03 cm

17.23 cm

11.25 cm

10.09 cm

answer is C.

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Detailed Solution

In the triangle ABC, we have

D E | | A C, D F | | A E

. Given that,

B F = 4 c m

… (1)

F E = 5 c m

… (2)
According to BPT, in

Δ B A E

, we have

D F | | A E

. So,

B D D A = B F F E B D D A = 45

According to BPT, in

Δ A B C

, we have

D E | | A C

. So,

B E E C = B D D A B E E C = 45

Writing BE as the sum of BF and FE, and we have

B F + F E E C = 45 4 + 5 E C = 45 9 E C = 45 E C = 9 (5) 4 E C = 11.25 c m

Hence, the correct option is 3.

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