Question

IN triangle ABC , angle B=90° , BD is perpendicular on AC , ar(ABC) = p and BC= a ,then prove that BD=2pa/√ 4p2 +a4.

Answer 1

Hey friend, Harish here.

Here is your answer.

REFER TO THE IMAGE FOR ANSWER.

NOTE:

1) $\mathrm{\frac{1}{2}\times Base\times Height = Area}$

It is given that BD is perpendicular to AC.

So here, BD becomes the height and AC becomes the base.

So this is now been used in the 5th line of the answer.

2) We have show that :

$\mathrm{BD = \frac{2A}{\sqrt{\frac{4A^2+a^4}{a^2}}}}$

Now using the property:  $\mathrm{\frac{a}{\big(\frac{b}{c}\big)} =\frac{ac}{b}}$

We are taking √(a²) to the numerator.

Hence Proved.

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Hope my answer is helpful to you.