Question

if the length of a diagonal in a square is a, what is the length of its side? answer:

Explanation:

Step1: Recall square diagonal formula

In a square, if side length is \( s \), diagonal \( d \) satisfies \( d = s\sqrt{2} \) (by Pythagorean theorem: \( s^2 + s^2 = d^2 \Rightarrow 2s^2 = d^2 \Rightarrow d = s\sqrt{2} \)).

Step2: Solve for side length \( s \)

Given \( d = a \), substitute into formula: \( a = s\sqrt{2} \). Solve for \( s \): \( s=\frac{a}{\sqrt{2}}=\frac{a\sqrt{2}}{2} \) (rationalize denominator).

Answer:

\(\frac{a\sqrt{2}}{2}\)