Math, asked by yuvisharma, 1 day ago

10. The value of h in the adjoining figure is: (a) 6 cm (b) 3 cm (c) 4 cm (d) can't be determined 14 cm 12 cm 7 cm​

Answers

Answered by mrigankadabnath
1

Answer:

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Question

In the adjoining figure, D is a point on BC such that ∠ABD=∠CAD. If AB=5 cm,AC=3 cm and AD=4 cm, find

(i) BC

(ii) DC

(iii) area of △ACD: area of △BCA.

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Solution

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From the question it is given that,

∠ABD=∠CAD

AB=5cm,AC=3cm and AD=4cm

Now, consider the △ABC and △ACD

∠C=∠C … [common angle for both triangles]

∠ABC=∠CAD … [from the question]

So, △ABC∼△ACD

Then, AB/AD=BC/AC=AC/DC

(i) Consider AB/AD=BC/AC

5/4=BC/3

BC=(5×3)/4

BC=15/4

BC=3.75cm

(ii) Consider AB/AD=AC/DC

5/4=3/DC

DC=(3×4)/5

DC=12/5

Dc=2.4cm

(iii) Consider the △ABC and △ACD

∠CAD=∠ABC … [from the question]

∠ACD=∠ACB … [common angle for both triangle]

Therefore, △ACD∼△ABC

Then, area of 

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