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
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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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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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