Question

a square has a diagonal measuring ( 6sqrt{2} ) inches. what is the perimeter of the square? enter your answer in the box.

Explanation:

Step1: Find the side length of the square

Let the side length of the square be \(a\). According to the Pythagorean theorem for a square (\(d^{2}=a^{2}+a^{2}\), where \(d\) is the diagonal), given \(d = 6\sqrt{2}\). Then \(d^{2}=(6\sqrt{2})^{2}=72\), and \(d^{2}=2a^{2}\). So \(2a^{2}=72\), \(a^{2} = 36\), \(a=6\) (since \(a>0\)).

Step2: Calculate the perimeter of the square

The perimeter formula of a square is \(P = 4a\). Substitute \(a = 6\) into the formula, \(P=4\times6\).

Answer:

\(24\)