Triangle ABC is a right angled triangle and BD =3cm,AB=4cm, and area of ABC=32, Then find area of ABD.

Asked by nitinkumarsingh.singh.75 | 16th Oct, 2015, 08:29: PM

Expert Answer:

C o n s i d e r space a space r i g h t space t r i a n g l e space A B C space r i g h t space a n g l e d space a t space B. D space i s space t h e space p e r p e n d i c u l a r space f r o m space B space t o space A C.
G i v e n space t h a t space A B equals 4 space c m space a n d space A r e a open parentheses triangle A B C close parentheses equals 32 space s q space c m. W e space k n o w space t h a t space t h e space a r e a space o f space a space r i g h t space t r i a n l g equals 1 half cross times b a s e cross times h e i g h t. H e r e comma space h e i g h t space i s space g i v e n space a s space A B equals 4 space c m rightwards double arrow 32 equals 1 half cross times B C cross times A B rightwards double arrow 64 equals B C cross times 4 rightwards double arrow B C equals 64 over 4 equals 16 space c m B y space a p p l y i n g space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma A B squared plus B C squared equals A C squared rightwards double arrow 4 squared plus 16 squared equals A C squared rightwards double arrow A C squared equals 16 plus 256 rightwards double arrow A C squared equals 272 rightwards double arrow A C equals 4 square root of 17  C o n s i d e r space t h e space t r i a n g l e s comma space triangle A B C space a n d space triangle A D B angle A B C equals angle A D B equals 90 degree angle B A C equals angle D A B space space space left square bracket c o m m o n right square bracket T h u s comma space A n g l e minus A n g l e space s i m i l a r i t y comma space w e space h a v e comma triangle A B C tilde triangle A D B H e n c e space t h e space c o r r e s p o n d i n g space s i d e s space a r e space p r o p o r t i o n a l. fraction numerator A B over denominator A C end fraction equals fraction numerator A D over denominator A B end fraction rightwards double arrow A B squared equals A C cross times A D rightwards double arrow 4 squared equals 4 square root of 17 cross times A D rightwards double arrow fraction numerator 4 over denominator square root of 17 end fraction equals A D A r e a space o f space t h e space t g r i a n g l e space A B D equals 1 half cross times B D cross times A D equals 1 half cross times 3 cross times fraction numerator 4 over denominator square root of 17 end fraction equals fraction numerator 6 over denominator square root of 17 end fraction s q u a r e space u n i t s

Answered by Vimala Ramamurthy | 17th Oct, 2015, 02:07: PM