F I N D space T H E space B A S E space O F space A N space I S O S C E L E S space T R I A N G L E space W H O S E space A R E A space I S space 12 C M squared space A N D space O N E space O F space E Q U A L space S I D E S space I S space 5 space C M.

Asked by harshmandlik | 11th Aug, 2014, 04:23: PM

Expert Answer:

O n e space o f space e q u a l space s i d e s space o f space a n space i s o s c e l e s space t r i a n g l e space i s space 5 space c m. T h e space a l t i t u d e space f r o m space t h e space v e r t e x space t o space t h e space b a s e space b i s e c t s space t h e space b a s e. L e t space x space b e space t h e space b a s e space o f space t h e space i s o s c e l e s space t r i a n g l e. C o n s i d e r space t h e space f o l l o w i n g space f i g u r e. space
H e r e comma space triangle A B C space i s space a n space i s o s c e l e s space t r i a n g l e space w i t h space v e r t e x space a t space A. T h e space a l t i t u d e space b i s e c t s space B C space a n d space h e n c e space B D equals D C equals x over 2 F r o m space t h e space r i g h t space t r i a n g l e space triangle A B D comma space b y space P y t h a g o r a s space T h e r o e m comma space w e space h a v e comma B D squared plus A D squared equals A B squared rightwards double arrow open parentheses x over 2 close parentheses squared plus A D squared equals 5 squared rightwards double arrow A D squared equals 25 minus x squared over 4 rightwards double arrow A D squared equals fraction numerator 100 minus x squared over denominator 4 end fraction rightwards double arrow A D equals fraction numerator square root of 100 minus x squared end root over denominator 2 end fraction T h e space a r e a space o f space triangle A B C equals 1 half cross times b a s e cross times a l t i t u d e G i v e n space t h a t space a r e a space o f space triangle A B C equals 12 space c m squared T h e r e f o r e comma space 12 equals 1 half cross times x cross times fraction numerator square root of 100 minus x squared end root over denominator 2 end fraction space rightwards double arrow 48 equals x square root of 100 minus x squared end root S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e 2304 equals x squared cross times open parentheses 100 minus x squared close parentheses rightwards double arrow x to the power of 4 minus 100 x squared plus 2304 equals 0 A s s u m e space x squared equals y ; space t h u s comma space w e space h a v e comma y squared minus 100 y plus 2034 equals 0 rightwards double arrow y squared minus 64 y minus 36 y plus 2304 equals 0 rightwards double arrow y open parentheses y minus 64 close parentheses minus 36 open parentheses y minus 64 close parentheses equals 0 rightwards double arrow open parentheses y minus 36 close parentheses open parentheses y minus 64 close parentheses equals 0 rightwards double arrow y equals 36 space o r space y equals 64 rightwards double arrow x squared equals 36 space o r space x squared equals 64 rightwards double arrow x equals 6 space o r space x equals 8 I f space t h e space b a s e space i s space 6 space c m comma space t h e n space t h e space h e i g h t space i s space square root of 100 minus 36 end root equals 8 space c m I f space t h e space b a s e space i s space 8 space c m comma space t h e n space t h e space h e i g h t space i s space square root of 100 minus 64 end root equals 6 space c m

Answered by Vimala Ramamurthy | 12th Aug, 2014, 09:18: AM