Question
Thu March 12, 2015 By: Balachandiran Ps

find three sides of a right triangle which forms a AP . whose sum is 24

Expert Reply
Vimala Ramamurthy
Thu March 12, 2015
L e t space a minus d comma a comma a plus d space a r e space t h e space t h r e e space t e r m s space w h i c h space f o r m s space a n space A P. G i v e n space t h a t space a minus d plus a plus a plus d equals 24 rightwards double arrow 3 a equals 24 rightwards double arrow a equals 24 over 3 rightwards double arrow a equals 8 A l s o space g i v e n space t h a t space a minus d comma a comma a plus d space f o r m s space t h e space s i d e s space o f space t h e space r i g h t space t r i a n g l e. T h u s comma space 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 open parentheses a minus d close parentheses squared plus a squared equals open parentheses a plus d close parentheses squared S u b s t i t u t i n g space t h e space v a l u e space a equals 8 space i n space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma open parentheses 8 minus d close parentheses squared plus 8 squared equals open parentheses 8 plus d close parentheses squared rightwards double arrow 64 plus d squared minus 16 d plus 64 equals 64 plus d squared plus 16 d rightwards double arrow 32 d equals 64 rightwards double arrow d equals 64 over 32 equals 2 T h u s comma space t h e space r e q u i r e d space A P space i s comma space 8 minus 2 comma 8 comma 8 plus 2 equals 6 comma 8 comma 10 T h u s comma space t h e space t h r e space s i d e s space o f space t h e space r i g h t space t r i a n g l e space a r e colon space 6 comma space 8 comma space 10
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