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ICSE Class X Math 2014 Solved Paper

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In △ABC,∠ABC=∠DAC.AB=8‌cm,AC= 4‌cm,AD=5‌cm.
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Question : 26
Total: 52
Find BC and CD
Solution:  
∵‌‌△ACD‌∼∆BCA
‌
AC
BC
=‌
CD
CA
‌=‌
AD
BA

⇒‌‌‌
4
BC
=‌
CD
4
‌=‌
5
8
‌∴‌‌‌
4
BC
=‌
5
8
‌ and ‌‌
CD
4
=‌
5
8
‌⇒‌‌BC=‌
4×8
5
=‌
32
5
=6.4‌cm.
and CD=‌
5
8
×4=‌
5
2
=2.5‌cm.
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