Question

12 fill in the blank 1 point what is the length of side s of the square shown below? 45° 8 90° s choose your answer.. choose your answer.. radical 8 1 4 radical 2 8 radical 2

Explanation:

Step1: Identify the triangle type

The triangle formed by the diagonal of the square is a 45 - 45 - 90 triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the hypotenuse \(c\) is related to the legs \(a\) (or \(s\) in this case) by the formula \(c = a\sqrt{2}\).

Step2: Solve for \(s\)

Given \(c = 8\), and \(c=s\sqrt{2}\). Then \(s=\frac{c}{\sqrt{2}}\). Rationalizing the denominator: \(s=\frac{8}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{8\sqrt{2}}{2}=4\sqrt{2}\).

Answer:

\(4\sqrt{2}\)