After filling the first sandbox to a height of 6 inches, the groundskeeper had 24 cubic feet of sand left over. She used all the leftover sand to fill the second sandbox.
. The second sandbox has a base in the shape of a rectangle.
The base of the second sandbox has a perimeter that is less than 35 feet.
The groundskeeper filled the second sandbox to a height of 6 inches.
What could be the length and width, in feet, of the second sandbox?

Length could be 14.05 ft and width 3.41 ft.

Step-by-step explanation:

The volume of the sand in the second box = 24 ft^3.

Let its base be x feet wide and y feet long.

Then  2(x + y) < 35.

The volume of sand = 0.5xy ft^3.

So 0.5xy = 24

xy = 48.

x = 48/y

Substituting ih the above inequality:

2(48/y + y) < 35

96/y + 2y < 35

2y^2 - 35y + 96 < 0

Solving 2y^2 - 35y + 96 = 0 gives y = 3.41, 14.09.

So the length  could be 14.05 ft and the width 48/14 = 3.41 ft.

length 8ft width 6ft

Step-by-step explanation: