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BD Perpendicular AC , AB =BC=a

Find the area of triangle ABC

enter image description here

I have tried Googling , I used formula 1/2 (base X Height) . Used Pythagorean theorem. Anyone can suggest me solution.

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perhaps i should say something more helpful, pythagoras theorem. – Lost1 May 18 '13 at 2:46
Thanks , i will workout ! – SSK May 18 '13 at 2:46
@Lost1, please let's be civil. – vadim123 May 18 '13 at 2:51
up vote 0 down vote accepted

Let $y$ represent the distance $CD$. Then $y^2+x^2=a^2$, or $y=\sqrt{a^2-x^2}$. Now you have enough to find the area of triangle $BCD$ using your area formula. Double this to find the area of the whole triangle.

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Found answer 2a.\sqrt{x^2-q^2}$. Thanks man you guys so supportive – SSK May 18 '13 at 2:57

With reference to comments: Let's be supportive.

If BD is a perpendicular, then you can split ABC into two right-angled triangles, so it is easier to work with:
enter image description here

Then you can use the formula $Area = \frac{1}{2}\cdot base \cdot height$ for each triangle, and add the two. You'll need to find the size of the base of each triangle using the pythagorean theorem.

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I have found answer 2a. Sqrt of x^2-a^2 – SSK May 18 '13 at 3:04

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