college algebra

Question

A rectangular piece of metal is 30 in 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?

Answer 1

l = 30 + w

squares with sides 6 inches are cut from all 4 corners, flaps folded up to form an open box

volume = 1050 cubic inches. what were the original dimensions of the metal. length and width??

volume = 6(l -12)(w-12) = 1050

(w+18)(w-12) = 1050/6 = 175

w^2 + 6w = 175 + 18(12)= 391

complete the square or use the quadratic formula

w^2 +6w + 9 = 400

(w+3)^2 = 20^2

w +3 = 20

w = 17 inches wide

l = 47 inches in length

cut 6 sided squared from the 4 corners

leaving w = 5 inches and l=35

v = 6(5)35 = 6(175) = 1050 in^3