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Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out 5-in squares from each corner. The length of the original piece of cardboard is 10 in more than the width. If the volume of the box is 1875 in3, determine the dimensions of the original piece of cardboard.

Lorene plans to make several opentopped boxes in which to carry plants She makes the boxes from rectangular sheets of cardboard from which she cuts out 5in squa class=


Answer :

The dimensions of the original shapes are 15 and 25 inches respectively

How to determine the dimensions

The formula for volume of a rectangle is expressed as;

Volume = length × width × height

From the information given, we have;

  • Length = y
  • Width = y + 10
  • Height = 5
  • Volume = 1875

Substitute the values

1875 = 5 × y × y + 10

Divide both sides 5

1875 / 5 = y(y + 10)

expand the bracket

375 = y² + 10y

y² +10y - 375 = 0

y² + 25y - 15y - 375 = 0

y(y + 25) - 15( y + 25) = 0

y= 15 or y = -25

If y = 15 Inches

Width = 15 + 10 = 25 Inches

Thus, the dimensions of the original shapes are 15 and 25 inches respectively

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