Question

6 practice 6 (from unit 4, lesson 2)
what is the length of the square’s side?
image of a square with a diagonal labeled 6
a 3 units
b \\(\frac{6}{\sqrt{2}}\\) units
c \\(6\sqrt{2}\\) units
d 12 units
how did i do?

Explanation:

Step1: Use Pythagorean theorem

Let the side length of the square be \(a\). In a square, the diagonal \(d\) and side \(a\) satisfy \(d^{2}=a^{2}+a^{2}\) (by Pythagorean theorem, since the two sides of the right - triangle formed by the diagonal are equal in a square). Given \(d = 6\), then \(6^{2}=2a^{2}\).

Step2: Solve for \(a\)

We have \(36=2a^{2}\), so \(a^{2}=\frac{36}{2}=18\), and \(a=\sqrt{18}=\frac{6}{\sqrt{2}}\) (rationalizing the denominator: \(a = \frac{6\sqrt{2}}{2}=3\sqrt{2}\), but also from \(a^{2}=\frac{36}{2}\), \(a=\frac{6}{\sqrt{2}}\)).

Answer:

B. \(\frac{6}{\sqrt{2}}\) units