Answer:
3in by 1in by 8in
Step-by-step explanation:
Volume of the box = Length × Width × Height
Given
Volume = 24in³
If the width is 2inhes less than the length
W = L-2... 2
Also if the height is 5 inches greater than the length, then;
H = L+5 ... 3
Substitite 2 and 3 into the formula.
V= LBH
24 = L(L+5)(L-2)
24 = L(L²+3L-10)
24 = L³+3L²-10L
L³+3L²-10L-24 =0
Factorize
The factored form is
(L+2)(L²+L−12) = 0
L²+L-12 = 0
L²+4L-3L-12 = 0
L(L+4)-3(L+4) = 0
(L+4) = 0 and L-3 = 0
L = 3in
W = L-2
W = 3-2
L = 1in
H = L+5
H=3+5
H = 8in
Hence the dimension is 3in by 1in by 8in
