Find the dimensions of the original piece of metal

Question

A rectangular piece of metal is 5 in. longer than it is side. Square with sides 2 in. long are cut

from the four corners, and the flaps are folded upward to form an open box. If specifications call for the

volume to be 64 in³, find the dimensions of the original piece of metal. (V=lwh)

Answer 1

Volume = 64 = 2(W)(W+5)

32 = W^2 +5W

W^2+5W-32=0

W^2+5W+25/4 = 32 + 25/4

(W+5/2)^2 = 153/4

W+5/2 = + or - (1/2)sqr153 = (1/2)(3)sqr17

W = -5/2 + or - (3/2)sqr17 = about -2.5 + or - 6.18, ignore the negative square root

W= 3.68

L=5+3.68 = 8.68

V=64 = 2 x 3.68 x 8.68 = 64 cubic inches rounded off to nearest integer

to get original dimensions of the rectangle, add 4 to W and 4 to L to get

7.68 by 12.68 inches