Answer: the cubic equation is
L^3 - 52L +144 =0
Lenght= 4inches
Width = 2inches
Height = 3 inches
Step-by-step explanation:
Let the lenght= L
Let the width = W
Let the height = H
Volume of the box = 24 cubic inch
Total surface area of the box = 52 sq. Inches
W = L/2
W, = 0.5L
Volume = L * B * H
Insert W = 0.5L
L * 0.5L * H = 24
0.5L^2 * H = 24
H = 24/0.5L^2
= 48/L^2
Surface area equation
2(L*W) + 2(L+H) + 2(W+H)= 52
Divide through by 2
(L*W) + (L+H) + (W*H) = 26
Insert W= 0.5L
(L*0.5L) + (L*H) + (0.5L*H) = 26
0.5L^2 + LH + 0.5LH = 26
0.5L^2 + 1.5LH = 26
Insert H = 48/L^2
0.5L^2 + 1.5*48/L = 26
0.5L^2 + 72/L = 26
Multiply through by L to get rid of the denominator
0.5L^3 + 72 - 26L = 0
0.5L^3 - 26L + 72 = 0
Multiply through by 2, we have
L^3 - 52L +144 =0
Try L= 4
4*3 -52(4)+ 144 =0
0= 0
(L - 4) is a factor of cubic equation
Therefore Length (L) = 4 inch
Recall that W= L/2
W= 4/2
W= 2 inches
H= 48/L*2
= 48/4*2
= 48/16
= 3 inches
