please answer this question

Asked by mac12303190 | 6th Mar, 2010, 12:15: AM

Expert Answer:

AB2 + BC2 = AC2

AB2 + b2 = AC2

A(ABC) = x = (b)(AB)/2 = (BN)(AC)/2  ..... (1)

(b)(AB)/2 = (BN)(AC)/2

AB/AC = BN/b   

Squaring both sides,

AB2/AC2 = BN2/b2

(AC2 - b2)/AC2 = BN2/b2

But AC = 2x/BN   ..... (1)

Hence,

(AC2 - b2)/AC2 = BN2/b2

1 - b2/AC2 = BN2/b2

1 - b2BN2/(4x2) = BN2/b2

1  = BN2(1/b2 + b2/(4x2))

BN2 =  b2(4x2)/(b4 +4x2)

= 4b2x2/(b4 +4x2)

Hence,

BN = 2bx/(b4 + 4x2)

Regards,

Team,

TopperLearning.

 

 

Answered by  | 6th Mar, 2010, 05:58: PM

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