Question

the dimensions of a cuboid are in the ration 5:3:1 and its total surface area is 414 cm sq., find its dimensions

Answer 1

hello this is answer

we have given that :
the dimension ( length , breadth ,height ) are in ratio 5 :3:1
and 
surface area of cuboid = 414 m²

we have to find:
length , breadth , height of cuboid = ?

solution:-
because dimension are in ratio 5 : 3:1 
let :
the length of cuboid = 5x
breadth of cuboid = 3x 
height of cuboid = 1x 

we know that :
surface area of cuboid = 2[ lb +bh + hl ]

here,

S. area = 414 

=> 2[ lb +bh + hl ] = 414 

=> 2* [ 5x*3x + 3x*1x +1x*5x ] = 414 m²

=> (15x² + 3x² + 5x² ) = 207 

=> 23x² = 207 

=> x² = 207 / 23 = 9

=> x = 3 

hence ;
the length of cuboid = 5x = 5*3 = 15m
breadth of cuboid = 3x = 3*3 = 9m 
height of cuboid = x = 3m 

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