6 AM Quiz (Problem Solving) Is the problem obvious?

Do you think Mr Kanbili is fair and Mr Ong should accept the suggestion?
2. Give an example to illustrate your stand.
3. Explain how you come to this conclusion (Hint: Use algebra).

Note that the quiz is not a compulsory activity.
It serves to stretch our mind a little to see how we apply what we learn in classrooms in real world :)

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1. Woah,seeing Kenneth do so much and so complicated...i guess I stand no chance :( ALL THE BEST KENNETH!

3. Area of Square Field:
40x40=1600
If a=40:
a*a=a^2
Area of Rectangular Field:
If Length of Rectangular Field is b
If Breadth of Rectangular Field is c.
b*c=bc
To make Breadth of Rectangular Field=Length of Rectangular Field
(b+c)/2=b/2+c/2
Area of Square Field(Originally Rectangular Field):
(b/2+c/2)(b/2+c/2)=(b^2+2bc+c^2)/4
Area of Rectangular Field(Originally Square Field):
New Length:a+x
Area of Rectangular Field to Square Field
(a/2-x/2+a/2+x/2)(a/2-x/2+a/2+x/2)
=a^2+a^2+a^2+a^2-ax-ax-ax+ax+ax+ax-x^2-x^2+x^2+x^2
=(4a^2)/4
=a^2(Original Area of Square Field)
OR
a+d=y(New Length of Square Field)
(x/2+y/2)^2=x^2+2xy+y^2
[Correction:This does not give like a final answer so the first option is better.]
Conclusion:Mr Ong should not accept the suggestion because the formula to get a Rectangular Field to a Square Field is not a final answer so that we do not know if the area of the square field(Originally the Rectangular Field) is a perfect square that means the length and breath added up together cannot be divided to 2.

1. You started well by computing the actual area proposed.
Next, could have used the fact that the rectangle formed through changes proposed/ made to the original length of the square.
That would have simplified your explanation as you only deal with one variable (as we had discussed in class)

4. The field is supposed to be 40m x 40m

Mr Kanbili says that what the rectangular field losses for going north , it gains in going east.

He is not fair .

Let a = meters to the north (breadth) and b = meters to the east (length)
Area of the square = a x b = ab

If a-1 then b must + 1 , so the area would be
(a-1 )x (b+1) = ab-1

If a-2 then b must + 2 , so the area will be
(a-2) x (b+2) = ab-2

As the breadth of the rectangle gets shorter and the length of the rectangle gets longer , the area of the field will decrease.

5. It's a good attempt to use algebra to explain.
You tried to vary the length that Mr Kanbili suggested to show there is a difference.
To keep it simple like what we had discussed in class, we could let the difference suggested by Mr Kanbili to be x in order to generalize our conclusion :)