The area of the adjacent faces of a rectangular block are in the ratio 2:3:4. It's volume is 9000cubic metre then find the length of the shortest edge
 

Asked by surajsugitha | 12th Nov, 2015, 07:33: PM

Expert Answer:

G i v e n space t h a t space t h e space a r e a s space o f space t h e space a d j a c e n t space f a c e s space o f space a space r e c tan g u l a r space b l o c k space a r e space i n space t h e space r a t i o space 2 colon 3 colon 4 L e t space l comma b space a n d space h space b e space t h e space d i m e n s i o n s space o f space t h e space r e c tan g u l a r space b l o c k. l equals l e n g t h comma space b equals b r e a d t h space a n d space h equals h e i g h t H e n c e space v o l u m e equals l cross times b cross times h space space space space space space space space space space space space space space space space space space space space space space space equals 9000 space m cubed space space space... open parentheses 1 close parentheses F r o m space t h e space g i v e n space s t a t e m e n t comma space w e space h a v e comma l cross times b colon b cross times h colon l cross times h equals 2 colon 3 colon 4 rightwards double arrow l cross times b equals 2 x... open parentheses 2 close parentheses b cross times h equals 3 x space... open parentheses 3 close parentheses a n d space l cross times h equals 4 x space space space... open parentheses 4 close parentheses N o w space c o n s i d e r space m u l t i p l y i n g space t h e space e q u a t i o n s space open parentheses 2 close parentheses comma space open parentheses 3 close parentheses comma space a n d space open parentheses 4 close parentheses comma space w e space h a v e comma l cross times b cross times b cross times h cross times l cross times h equals 2 x cross times 3 x cross times 4 x rightwards double arrow l squared cross times b squared cross times h squared equals open square brackets 2 x cross times 3 x cross times 4 x close square brackets rightwards double arrow open square brackets l cross times b cross times h close square brackets squared equals open square brackets 2 cross times 3 cross times 4 cross times x cubed close square brackets rightwards double arrow open square brackets l cross times b cross times h close square brackets squared equals open square brackets 24 cross times x cubed close square brackets rightwards double arrow open square brackets 9000 close square brackets squared equals open square brackets 24 cross times x cubed close square brackets space space... open parentheses f r o m space e q u a t i o n space open parentheses 1 close parentheses close parentheses rightwards double arrow 24 cross times x cubed equals 81000000 rightwards double arrow x cubed equals 81000000 over 24 rightwards double arrow x cubed equals 3375000 rightwards double arrow x equals 150 T h u s comma space l cross times b equals 2 cross times 150 equals 300... open parentheses 5 close parentheses b cross times h equals 3 cross times 150 equals 450... open parentheses 6 close parentheses l cross times h equals 4 cross times 150 equals 600... open parentheses 7 close parentheses D i v i d i n g space e q u a t i o n space open parentheses 5 close parentheses space b y space e q u a t i o n space open parentheses 6 close parentheses comma space w e space h a v e comma l over h equals 300 over 450 equals 2 over 3... open parentheses 8 close parentheses D i v i d i n g space e q u a t i o n space open parentheses 6 close parentheses space b y space e q u a t i o n space open parentheses 7 close parentheses comma space w e space h a v e comma b over l equals 450 over 600 equals 3 over 4... open parentheses 9 close parentheses D i v i d i n g space e q u a t i o n space open parentheses 5 close parentheses space b y space e q u a t i o n space open parentheses 7 close parentheses comma space w e space h a v e comma b over h equals 300 over 600 equals 1 half... open parentheses 10 close parentheses F r o m space e q u a t i o n space open parentheses 9 close parentheses comma space w e space h a v e comma b equals fraction numerator 3 l over denominator 4 end fraction S u b s t i t u t i n g space t h e space v a l u e space b equals fraction numerator 3 l over denominator 4 end fraction space i n space e q u a t i o n space open parentheses 5 close parentheses comma space w e space h a v e comma l cross times fraction numerator 3 l over denominator 4 end fraction equals 300 rightwards double arrow 3 l squared equals 4 cross times 300 rightwards double arrow l squared equals fraction numerator 4 cross times 300 over denominator 3 end fraction rightwards double arrow l squared equals 400 rightwards double arrow l equals 20 space m rightwards double arrow b equals fraction numerator 3 cross times 20 over denominator 4 end fraction rightwards double arrow b equals 15 space m S u b s t i t u t i n g space t h e space v a l u e space b equals 15 space i n space e q u a t i o n space open parentheses 10 close parentheses comma space w e space h a v e comma 15 over h equals 1 half rightwards double arrow h equals 30 space m T h u s space t h e space l e n g t h space o f space t h e space s h o r t e s t space e d g e left parenthesis w i d t h right parenthesis equals 15 space m  space space space

Answered by Vimala Ramamurthy | 13th Nov, 2015, 10:46: AM