In ∆ABC, it is given that DE || BC. If AD=3cm, DB=2cm, DE=6cm, then find BC.
Answers
Answer:
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Step-by-step explanation:
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
\begin{gathered}\frac{AD}{AB} = \frac{DE}{BC}\\\frac{3}{5} = \frac{6}{BC} \\BC = (5)(2) = 10 cm\end{gathered}
AB
AD
=
BC
DE
5
3
=
BC
6
BC=(5)(2)=10cm
Answer:
10 cm
Step-by-step explanation:
bc=5×2=10
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