Question

in triangle abc it is given that DE parallel BC if AD = 3 cm DB=2cm and DE= 6cm then find BC

Answer 1

Since DE || BC,

. : AD/DB = AE/EC

⇒ AD/AB = AE/AC

Also, ∠DAE = ∠BAC (Common)

ΔADE ~ ΔABC (SAS Similarity Criterion)

⇒ AD/AB = DE/BC = AE/AC (Sides are proportional)

⇒ 3/5 = 6/BC

⇒ BC = 10 cm

Answer 2

BC = 10 cm

• Given,

              AD = 3 cm, DB = 2 cm, DE = 6 cm

               AB = AD + DB = 3 + 2 = 5 cm

• Given,  

               DE║BC   AB is the transversal

           ⇒ ∠ADE = ∠ABC   [∵ pair of corresponding angles]   ------(1)

• Similarly, if AC is transversal

           ⇒ ∠AED = ∠ACB     [∵ pair of corresponding angles]   -----(2)

• In ΔABC, ΔADE,

               ∠ADE = ∠ABC        [From (1)]

               ∠AED = ∠ACB        [From (2)]

               ∠DAE = ∠BAC        [common angle]

• Since all three angles are equal,corresponding sides will be proportionate

                 $\frac{AD}{AB} = \frac{DE}{BC}\\\frac{3}{5} = \frac{6}{BC} \\BC = (5)(2) = 10 cm$