Question

Consider six squares with sides of different lengths. The length of the side of a square is proportional to:

• A. Perimeter of the square
• B. Area of the square
• C. Both of these
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A

Perimeter of the square

C

Both of these

If two things are proportional that indicates their ratio will be constant. Now, let's verify options.

$\frac{Lengthofsquare}{Perimeterofsquare}=\frac{a}{4a}=\frac{1}{4}$
which is a constant.

$\frac{Lengthofsquare}{Areaofsquare}=\frac{a}{a^2}=\frac{1}{a}$
which is not constant and varies with side of square.

$\frac{Lengthofsquare}{Lengthofdiagonal}=\frac{a}{\sqrt{2}a}=\frac{1}{\sqrt{2}}$
which is constant.

Hence, the length of the side of a square is proportional to its perimeter and diagonal.