what is the original width? what is the original length?

Question

A rectangular piece of metal is 30in longer than it is wide. Squares with sides 6

in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1050 in ^3​,

what were the original dimensions of the piece of​ metal?

what is the original width

Answer 1

V = volume = 1050 = 6(L-12)(L-30-12) = 6(L^2-52L+504)

L^2 -54L +504 = 1050/6 = 175

L^2 -54L = 175-504 = -329

L^2 -54L + 27^2 = -329 + 27^2

(L-27)^2 = 729-329 = 400

L-27 = + or - 20

L= 27 + 20 = 47

W = 47-30 = 17

dimensions are 47 x 17 inches

subtract 12 from each to get a box with

length = 35 x width 5 x 6 depth = 1050 cubic inches

volume = 6 x 35 x 5 = 1050