A box has a certain length, width, and height. The length of the box is equal to twice its width, as well as equal to 5 less than its height. If the total surface area of the box is 234, then what is the height of the box?

Lilliam0216 Apr 3, 2024

#1**+1 **

L = H - 5

H = L + 5

L = 2W

W = L/2

W = ( H - 5) / 2

SA = 2 [ LW + HL + HW ]

234 = 2 [ (H - 5)(H - 5)/2 + H(H -5) + H (H - 5) / 2 ]

234 = (H - 5)(H-5) + 2H (H -5) + H(H -5)

234 = H^2 - 10H + 25 + 2H^2 - 10H + H^2 - 5H

4H^2 - 25H + 25 = 234

4H^2 - 25H - 209 = 0

H = [25 + sqrt [ 625 - 4*4 * -209 ] ] / 8 = [25 + sqrt [ 3969 ] / 8 = [25 + 63 ] / 8 = 88 / 8 = 11

CPhill Apr 4, 2024