KCC's Quizzes AQQ261 about a rectangle area

The area of ABCD is 96.

You see that (y-8)*y=9, from which you get y=9 (the other solution of the quadratic equation is negative). Then x= (y-8)+(y+2)-->x=12. So BC=12 and AB=8, from which you get the result.

Figure is not consistent with the data.

The area of ABCD is 96.

You see that (y-8)*y=9, from which you get y=9 (the other solution of the quadratic equation is negative). Then x= (y-8)+(y+2)-->x=12. So BC=12 and AB=8, from which you get the result.

Figure is not consistent with the data.

Félicitation gpiarino correct! (such quiz is too easy for people like you...)

Hi gpiarino , I was too fast when granting you the right answer... 96 CANNOT be the area of the big rectangle. Look: in your equations you will have y=9 while the entire segment AB is only 8 which is visibly impossible!

Yes, I mentioned the inconsistency between data and figure. If you want to avoid that, you need to assign a higher than 9 value to the area in grey. For example, if this area is 65, you get y=13 and x=20 and AB=16 is then longer than y and everything appears "normal". ABCD area would be 320 in this case. 

In fact, the equations used are valid. They only conclude to something that include the acceptance of negative length and negative area. That's OK in a pure math world, but not in our physical world. Lesson is: machine or simulator can never completely replace the human common sense....