The hypotenuse of a right angled triangle is 3sqrt (5).if the smaller side is tripled and the larger side is doubled,then the new hypotenuse will be 15 cm.find the length of each side.

Asked by nitinkumarsingh.singh.75 | 1st Aug, 2015, 12:59: PM

Expert Answer:

begin mathsize 16px style L e t space t h e space s m a l l e r space s i d e space f space r i g h minus a n g l e space t r i a n g l e space b e space a space c m space a n d space l a r g e r space s i d e space b e space b space c m. H y p o t e n u s e equals 3 square root of 5 B y space p y t h a g o r a s space t h e o r e m comma a squared plus b squared equals open parentheses 3 square root of 5 close parentheses squared rightwards double arrow a squared plus b squared equals 45 space space space space space space space.... left parenthesis i right parenthesis N o w comma space a c c o r d i n g space t o space g i v e n space i n f o r m a t i o n comma W h e n comma space s m a l l e r space s i d e equals 3 a comma space l a r f e r space s i d e equals 2 b comma h y p o t e n u s e equals 15 c m left parenthesis 3 a right parenthesis squared plus left parenthesis 2 b right parenthesis squared equals left parenthesis 15 right parenthesis squared 9 a squared plus 4 b squared equals 225 space space space space space space space.... left parenthesis i i right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis i right parenthesis space b y space 4 space 4 a squared plus 4 b squared equals 180 space space space space space left parenthesis i i i right parenthesis S u b t r a c t i n g space left parenthesis i i i right parenthesis space f r o m space left parenthesis i i right parenthesis 5 a squared equals 45 a squared equals 9 a equals 3 S u b s t t u i n g space i n space left parenthesis i right parenthesis comma left parenthesis 3 right parenthesis squared plus b squared equals 45 9 plus b squared equals 45 b squared equals 36 b equals 6  T h u s comma space t h e space l e n g t h space o f space s m a l l e r space s i d e space i s space 3 space c m space a n d space t h a t space o f space l a r g e r space s i d e space i s space 6 space c m. end style

Answered by Rashmi Khot | 2nd Aug, 2015, 03:38: PM