Question

1. what is the side length in this square?

a. 3 units
b. \\(\frac{6}{\sqrt{2}}\\) units
c. \\(6\sqrt{2}\\) units
d. 12 units
(there is a square with a diagonal labeled 6 on the right side of the question)

Explanation:

Step1: Relate side, diagonal of square

For a square with side length $s$, diagonal $d = s\sqrt{2}$

Step2: Solve for side length

Rearrange formula: $s = \frac{d}{\sqrt{2}}$. Substitute $d=6$:
$s = \frac{6}{\sqrt{2}} = \frac{6\sqrt{2}}{2} = 3\sqrt{2}$
Rationalize $\frac{6}{\sqrt{2}}$: $\frac{6}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 3\sqrt{2}$, which equals $\frac{6}{\sqrt{2}}$

Answer:

B. $\frac{6}{\sqrt{2}}$ units