Question

in the figure, given above, AB,CD,EF are parallel lines. Given AB=7.5cm,BC= xcm and CE =3cm, calculate values of X and y​

Answer 1

Answer:

X= 5 cm

Y =45/16 cm

Step-by-step explanation:

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in ∆BCD and ∆ BEF,

∠DBC =∠FBE ( common angle)

∠BCD = ∠BEF ( corresponding angles of parallel lines CD and EF )

∠BDC = ∠BFE ( corresponding angles of parallel lines CD and DF)

thus, ∆ BCD ≌ ∆ BEF ( A-A-A rule)

Hance, BC/ BE = BD/BF = CD/ EF ( corresponding sides )

x/ x+3 = BD/EF = y/4.5. ---- (i)

Similarly, ∆FCD ≌ ∆FAD

y/7.5 = DF/BF ---(ii)

From I and ii

BD = y/4.5 BF and DF = y/ 7.5 BF

BD+ DF = BF

y/4.5 BF + y/ 7.5 BF = BF

7.5y +4.5y = 7.5 × 4.5

y = 45/16

Also,

x/ x+3 = y/ 4.5

x/ x+3 = 45/ 16× 4.5

x/ x+3 = 45/ 72

72x = 45x + 135

27x = 135

x = 5cm