Let x be the sides of the square metal sheet.Since `5xx5` cm is cut on each corner of the metal sheets to form an open box, then the dimensions of the box is:length = x-10width = x-10 and height = 5 Since the volume of the box...

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Let x be the sides of the square metal sheet.

Since `5xx5` cm is cut on each corner of the metal sheets to form an open box, then the dimensions of the box is:

length = x-10

width = x-10 and

height = 5

Since the volume of the box is given, apply the formula of volume to solve for x.

`V=l*w*h`

`500=5(x-10)(x-10)`

To simplify, divide both sides by 5.

`500/5=(5(x-10)(x-10))/5`

`100=(x-10)(x-10)`

FOIL right side.

`100=x^2-10x-10+100`

`100=x^2-20x+100`

Set one side equal to zero.

`100-100=x^2-20x+100-100`

`0=x^2-20x`

Then, factor right side.

`0=x(x-20)`

Next, set each factor equal to zero and solve for x.

`x=0` and `x-20=0`

`x=20`

Since x represents the length of the sides of the square metal sheet, consider only the value of x that is greater than zero.**Hence, the dimension of the square metal sheet is `20xx20` cm.**