Answer:
Length = Width = Height = 64 ; Luggage Box is a CUBE
Step-by-step explanation:
Given : Length (L) + Width (W) + Height (H) ≤ 192 ; & Length = Width
Volume ( V )of luggage [Cuboid] = L.W.H
Since L = W :
V = L.L.H → V = L^2H
L + L + H = 192 → 2L + H = 192 → H = 192 - 2L
Putting value of 'H' in 'V'
V = L^2 (192 - 2L) → V = 192L^2 - 2L^3
Maximising volume function , differentiating it w.r.t 'L'
dV / dL = 2(192 L) - 3 (2L^2) → = 384L - 6L^2
dV / dL = 384L - 6L^2 = 0
384L = 6L^2 → 384 = 6L
L = 384 / 6 → L = 64 ; W also = 64
Putting value of L in 1st given sum equation : 2L + H = 192
2 (64) + H = 192
128 + H = 192 → H = 192 - 128 → H = 64
Since L = W = H = 64 ; Luggage bag is a Cube
