Question

If the area of a square
a square is four times its perimeter then
Calculate the length of side of the square.​

Answer 1

Step-by-step explanation:

Normally we would go about the answer in this way,

Let side of the square = x units

So area = X2 units2

Perimeter = 4x units

given that , area is 3 times the perimeter so,

X2 unit2 = 12x unit

=> x is either 12 or 0 . But since we don’t consider 0 to be an actual length so 12 unit should be the right answer.

Right?

Actually no. The question itself is fundamentally flawed.

Consider reverse engineering the question and this time lets take proper units.

Lets say metre.

Okay so side of square is 12m .

So area = 144 m2

and Perimeter = 48 m

Now if we take the ratio , 144 m2 / 48m = 3 m

Wait,what? How did we end up with a unit for a ratio ?

Here’s where the catch is. The question is flawed because of the comparison of wrong dimensions. When we ended up with an answer of 12 , the equation already had the unit defined for x, but at the end , we generally tend to include the unit again. Thus we end up with wrong dimensions. This is valid in case of general units as well :-

Say , 12 units was the side.

So area = 144 unit2

Perimeter = 48 unit

So ratio = 144 unit2 / 48 unit = 3 unit

Had it been the same dimension,i.e, the area , (say of another square or itself with adjusted length), the ratio and dimension would have ended up correctly.

Normally it is in human nature to ignore the the units while performing calculations. But we must take note that units may some time cause invalid dimensional comparison thus rendering the problem invalid/flawed.

Answer 2

Answer:

16

Step-by-step explanation:

x^2 = 4(4x)

(x is the side of square)

solving, x= 16