Question

If DE||BC, then find x
AD =3cm
DB=4cm
BC = 14cm

Answer 1

Answer:

6 cm

Step-by-step explanation:

It is given that DE ║ BC

∴ $\frac{AD}{DB}$ = $\frac{AE}{EC}$  (By Basic Proportionality Theorem)

⇒ $\frac{DB}{AD}$ = $\frac{EC}{AE}$

⇒ $\frac{DB}{AD}$ + 1 = $\frac{EC}{AE}$ + 1

⇒ $\frac{DB+AD}{AD}$ = $\frac{EC+AE}{AE}$

⇒ $\frac{AB}{AD}$ = $\frac{AC}{AE}$

⇒ $\frac{AD}{AB}$ = $\frac{AE}{EC}$  (Sides are proportional)

∠ A = ∠ A   (Same angle)

∴ Δ ADE is similar to Δ ABC  (SAS Similarity Criterion)

∴ $\frac{AD}{AB}$  =  $\frac{DE}{BC}$  (CPCT)

⇒  $\frac{3}{4+3}$ = $\frac{DE}{14}$

⇒ $\frac{3}{7}$ =  $\frac{DE}{14}$

⇒ 14 × 3  = 7 DE

⇒ 42 = 7 DE

⇒ $\frac{42}{7}$ = DE

⇒ 6 = DE

∴ DE = 6 cm

           

Answer 2

Given : DE || BC

AD = 3cm, BD = 4cm and BC= 14 cm

To Find : DE

Solution:

DE || BC

=> ∠D = ∠B    Corresponding angles are equal

   ∠E = ∠C     Corresponding angles are equal

=> ΔADE ~ Δ ABC  using AA similarity

Ratio of corresponding sides of similar triangle is equal

Hence  DE/BC = AD / AB

=> DE/ 14 = 3 /(AD + BD)

=> DE/14 = 3/(3 + 4)

=> DE/14 = 3/7

=> DE = 6  

Hence length of DE = 6 cm

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