Answer:
x = 1.64 in the size of the side of the square
Step-by-step explanation:
Let call x side of the square to be cut from cornes, then:
First side of rectangular base
L = 14 - 2*x
And the other side
d = 8 -2*x
Then Volume of the box
V(b) = L*d*x
V(x) = ( 14- 2*x ) * ( 8 -2*x)*x
V(x) = ( 112 - 28*x -16*x + 4*x² )*x ⇒ 4*x³ - 44*x² + 112*x
Taking derivatives on both sides of the equation we get:
V´(x) = 12*x² - 88*x +112
V´(x) = 0 ⇒ 12*x² - 88*x +112 = 0
A second degree equation, solvin it
3x² - 22*x + 28 = 0
x₁,₂ = [ 22 ± √484 - 336 ] / 6
x₁ = (22 + 12,17) /6 x₂ = ( 22 - 12.17 ) / 6
x₁ = 5.69 We dismiss this solution since it make side 8 - 2x a negative length
x₂ = 9.83/6
x₂ = 1.64
Then x = x₂ = 1.64 in
