Answer
12 in by 12 in
Step-by-step explanation
The original length = x
This makes the length of the cube made to be = x - (2×2)
= (x - 4) in
height of the cube = 2 in
Volume of the cube = (x - 4) × (x - 4) × 2 = 128
= (x² - 8x + 16) × 2 = 128
= 2x² - 16x + 32 = 128
= 2x² - 16x + 32- 128=0
= 2x² - 16x - 96 = 0
= x² - 8x - 48 = 0
lets use the factor method to solve the quadrilatic equation above,
x² - 8x - 48 = 0
proctuct = -48
sum = -8
The two factors are; -12 and 8.
(x + 8)(x - 12) = 0
So the value of x are 12 and -8. Since x is a length, it can not be negative.
∴ x = 12 in.
The original dimensions of the sheet are 12 in by 12 in.