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...
View This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.
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.