Question

. In triangleABC E divides AB in the ratio 1:3 and also F divides AC in the ratio 1:3,
EF = 2.8 cm. Find BC =​

Answer 1

Answer:

Let Area of ΔBEF=x

∴ Area of ΔAFE=3x

Let Area of ΔABF=3y

∴ Area of ΔCAF=2y

Area ΔABC= Area ΔBEF+ Area ΔAEF

3y=x+3x            (i)

3y=4x

43​=yx​

AreaΔABCAreaΔBEF​=yx​=51​×43​=203

Answer 2

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E/AB = AF / AC and

∠BAC = ∠EAF

Triangle ABC similar to triangle AEF (SAS)

by CPCT

EF is parallel to BC

AB: AE = BC/EF

Let l be the length of AB

the AE = l/4

1:(1/4) = BC:2.8

L/(L/4) = BC/2.8

BC = 2.8 X 4 = 11.2m