Question

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Question is in the attachment

Answer 1

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Answer 2

Answer:

(i) In Triangle ABC and EDC,

angle B = angle D ( corresponding angles)

angle C = angle C (same angle)

angle A = angle E (corresponding angles)

∴ by AAA similarity criteria, Triangle ABC and EDC are similar.

(ii) In triangle EDC and ABC,

BD/BC= 1/3

∴ BC/DC = 3/2

⇒ AB/DE = 3/2

12.3/DE = 3/2

DE = 24.6/3

DE = 8.2cm

(iii) ar (EDC)/ar(ABC) = (1/2×ED×h)/(1/2×AB×h)

(Draw M on Ab such that CM is altitude and N on ED such that CN is altitude)

= ED×CN/AB×CM (take as eq1)

Since triangle ABC is similar to triangle EDC,

AB/ED = BC/DC = AC/EC = CM/CN = 3/2

Sub eq1 ∴ ED×ED/AB×AB = ar(EDC)/ar(ABC)

= ED²/AB² = 2²/3² (Proportionality)

Thus, ar(EDC)/ar(ABC) = 4/9

Refer area proportionality theorem