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Question

In the following figure ABC=90 and BDAC. If AD=8 cm,CD=2 cm, then the length of BD is:
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A
4 cm
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B
8 cm
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C
16 cm
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D
10 cm
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Solution

The correct option is A 4 cm
Given that:
ABC=90,BDAC,AD=8cm,CD=2cm
To find:
BD=?
Solution:
In ABC,
AC=AD+DC=8cm+2cm=10cm
By Pythagorean theorem,
AB2+BC2=AC2
or, AB2+BC2=(10)2cm2
or, AB2+BC2=100cm2 ..............(i)
In ADB,
By Pythagorean theorem,
AD2+BD2=AB2
or, (8cm)2+BD2=AB2
or, 64cm2+BD2=AB2 ..............(ii)
In BDC,
By Pythagorean theorem,
CD2+BD2=BC2
or, (2cm)2+BD2=BC2
or, 4cm2+BD2=BC2 ..............(iii)
From eqn.(i),(ii) and (iii) we get,
64cm2+BD2+4cm2+BD2=100cm2
or, 68cm2+2BD2=100cm2
or, 2BD2=100cm268cm2
or, 2BD2=32cm2
or, BD2=16cm2
or, BD=4cm
Therefore, A is the correct option.

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