Question

the sum of the lengths of the edges of a cube is equal to half of the perimeter of a square.if the numerical value of the volume of the cube is equal to one sixth of the numerical value of the area of the square,then the length of one side of the square is​

Answer 1

let length of edge of cube be x

length of side of square be y

according to 1 condition

12x=1/2*4y

12x=2y

6x=y................eq 1

according to 2nd condition

x*x*x=1/6*y*y

y/6*y/6*y/6=1/6 *y*y

y/36=1

y=36

Answer 2

Side of Square  = 36  unit

Step-by-step explanation:

Let say cube Edge = c

the sum of the lengths of the edges of a cube = 12c

Let say side of square = s

Then Perimeter of Square  = 4s

12c  = 4s/2

=> c = s/6

Volume of cube  =  c³

Area of square  = s²

c³  = s²/6

=> (s/6)³ = s²/6

=> s³/6³ = s²/6

=> s = 36

Side of Square  = 36  unit

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