Consider six squares with sides of different lengths.The length of side of squ

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Consider six squares with sides of different lengths.The length of side of square is in direct proportion to:

Options:

A . Perimeter of the square

B . Area of the square

C . Diagonal of square

D .

\frac{P e r i m e t e r o f s q u a r e}{A r e a o f s q u a r e}

Answer: Option A
:
A and C

$\frac{L e n g t h o f s q u a r e}{P e r i m e t e r o f s q u a r e} = \frac{a}{4 a} = \frac{1}{4}$
which is a constant.

$\frac{L e n g t h o f s q u a r e}{A r e a o f s q u a r e} = \frac{a}{a^{2}} = \frac{1}{a}$
which is not constant.
$\frac{L e n g t h o f s q u a r e}{L e n g t h o f d i a g o n a l} = \frac{1}{\sqrt{2}}$
which is constant.

Hence, length of a square is in direct proportion with its perimeter and diagonal.

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