KCC's Quizzes AQQ261 about a rectangle area

Area = 48

Area = 48

math error.  Area=96

Thanks TimW ! Indeed, 96 seems to be the right solution but it will imply several abnomalies. Verify what would be the length y versus the entire segment AB...

Methodology:

1) Area of shaded box = y*(y-8) = 9.  Solving the resultant quadratic yields y=+9, -1.  Using y=9

2) side AD = 2y-6, thus length AD = 12

3) Total area = (2y-6)(x-4) = 2xy-6x-8y+24

4) substitute y=9 --> 18x-6x-72+24 --> 12x-48

5) since x = BC = AD = 12

6) area = 12(12)-48 = 144-48 = 96

Methodology:

1) Area of shaded box = y*(y-8) = 9.  Solving the resultant quadratic yields y=+9, -1.  Using y=9

2) side AD = 2y-6, thus length AD = 12

3) Total area = (2y-6)(x-4) = 2xy-6x-8y+24

4) substitute y=9 --> 18x-6x-72+24 --> 12x-48

5) since x = BC = AD = 12

6) area = 12(12)-48 = 144-48 = 96

Many thanks TimW for your detailed development! But I am afraid you have fallen in the same trap than many of us (including myself). All your equations and the final result 96 are correct... But only in a pure "math world"... In effect, for example, you came with y=9 but the entire segment AB is only 8; which is visibly impossible...

Why can that happens? Well with the data given there are negative lengths and negative area: that's fine for pure math but not in our real world. The lesson here is the human common sense cannot replaced by any software or robot...