A package has a width of 3 inches, it's height is 3 inches longer than its length. If the volume of the box is 390 cubic inches, what is the length and height of the package.

Let l be length of package.

Height , h = l + 3

Width , w = 3 in

Now,

Volume , V = lwh

390= l*3*(l+3)

130 = l*(l+3)

130 = l² + 3l

l² + 3l - 130 = 0

l² + 13l -10l - 130 = 0

l(l + 13) - 10(l +13) = 0

( l + 13)(l -10) = 0

l + 13 = 0 or l - 10 =0

l = -13 or l = 10

Now,

Length cannot be negative.

Therefore,

l = 10

Length = 10 in

Height , h = l + 3 = 10 + 3 = 13 in (answer)