In ΔABC, m∠B = 90, AB = BC. Then AB : AC = ......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 1:3
(b) 1:2
(c) 1:√2
(d) √2:1
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1:√2 is the correct answer
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In ∆ABC , <B = 90° ,
AB = BC
Therefore ,
<C = <A ----- ( 1 )
[ Since ,
Angles opposite to equal sides are
equal ]
<A + <B + <C = 180°
[ Angle sum property ]
<C + 90° + <C = 180° [ from ( 1 ) ]
=> 2<C = 180° - 90°
=> <C = 90/2
=> <C = 45°
Now ,
In ∆ABC ,
SinC = AB/AC
=> Sin 45° = AB/AC
=> 1/√2 = AB/AC
Therefore ,
AB : AC = 1 : √2
option ( c ) is correct.
••••
AB = BC
Therefore ,
<C = <A ----- ( 1 )
[ Since ,
Angles opposite to equal sides are
equal ]
<A + <B + <C = 180°
[ Angle sum property ]
<C + 90° + <C = 180° [ from ( 1 ) ]
=> 2<C = 180° - 90°
=> <C = 90/2
=> <C = 45°
Now ,
In ∆ABC ,
SinC = AB/AC
=> Sin 45° = AB/AC
=> 1/√2 = AB/AC
Therefore ,
AB : AC = 1 : √2
option ( c ) is correct.
••••
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