Question

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

• A. Perimeter of the square
• B. Area of the square
• C. Diagonal of square
• D. $\frac{Perimeterofsquare}{Areaofsquare}$

Answer 1

Answer: (A), (C)

Diagonal of square

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

$\frac{Lengthofsquare}{Areaofsquare}=\frac{a}{a^2}=\frac{1}{a}$
which is not constant.

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

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