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ICSE Class X Math 2015 Solved Paper

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ABC is a right angled triangle with ∠ABC= 90∘.D is any point on AB and DE is perpendicular to AC. Prove that :
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Question : 48
Total: 52
If AC=13‌cm,BC=5‌cm and AE=4 cm . Find DE and AD .
Solution:  
‌ In ‌△ABC,
(AC)2‌=(AB)2+(BC)2
169‌=(AB)2+25
AB‌=12‌cm
∵‌△ADE‌∼∆ACB
∴‌‌‌
DE
BC
=‌
AD
AC
‌=‌
AE
AB

∴‌‌‌
DE
BC
‌=‌
AE
AB

‌
DE
5
‌=‌
4
12

DE‌=‌
20
12
=‌
5
3
=1.67‌cm.
Now,
‌
AD
AC
‌=‌
AE
AB

‌
AD
13
‌=‌
4
12

AD‌=‌
13×4
12
=‌
13
3

‌=4.33‌cm.
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