Question

If side of square is decreased by 3 times, its area is decreased by :
a) One - Third
b) Two - Thirds
c) Two ninths
d) One - Ninth


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Answer 1

Answer:

D) One - Ninth

Step-by-step explanation:

Originally, let the side of the square be 's'

We know that:

   Area of square = (side)²

⇒ Area of square = s²     ---  {Equation 1}

If the side of the square is decreased by 3 times then,

$\maltese \: \: \boxed{\sf{New\: side \: formed = \dfrac{s}{3}}}$

Now, the area of this square with new side would be:

$\sf{Area_{(new\:square)}=\bigg(\dfrac{s}{3}\bigg)^{2}}$

$\implies \sf{Area\:of \: new\: square = \dfrac{s^{2}}{9}}$

$\implies \sf{Area\:of \: new\: square = s^{2} \times \dfrac{1}{9}\qquad\dashrightarrow \: \: Eq^{n}\:(2)}$

     

On comparing Equation 1 and Equation 2, we see that the area of the new square is decreased by 9 times

∴ The area of square is decreased by

One - Ninth.

Answer 2

Option d) One - Ninth.

Refer to the attachment

Hope it helps uh !