Question

Help me with this asap

Answer 1

If you begin with 1.5 yd^3 of topsoil and want the topsoil to be only 4 inches deep, then the area of the garden can be found as follows:

Convert 4 in to yards:    4 in       1 yd
                                     ------- * ----------- =  (1/9) yd
                                         1        36 in

The dimensions of the garden are x (width) by 2x (length) by (1/9) yd (depth).  The volume of topsoil would be 2x^2/9 = 1.5 yd^3.

Solving for x:   (2/9)x^2 = 1.5 yd^3, or   x^2 = (1.5 yd^3) (9/2)

Then:    x = sqrt(6.75 yd^3) = 2.6 yd    and    2x = 5.2 yd

Check:  Does (2.6 yd)(5.2 yd)(1/9) = 1.5 cu yd?  YES

Thus, the max size of the garden would be 2.6 yd wide, 5.2 yd long, and 4 inches (or 1/9 foot) deep.