Question

Solve the problem given below

Answer 1

X=12, the box when assembled is 2 inches tall and 8 inches long

Answer 2

Answer

12 in by 12 in

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.