Question

11 fill in the blank 1 point what is the length of the diagonal of the square shown below? 5 45° 5 5 90° 5 choose your answer... choose your answer... 25 5 radical 2 5 radical 5

Explanation:

Step1: Apply Pythagorean theorem

In a square, the diagonal \(d\) forms a right - triangle with two sides \(a = 5\) and \(b = 5\). The Pythagorean theorem is \(d^{2}=a^{2}+b^{2}\).
Substitute \(a = 5\) and \(b = 5\) into the formula: \(d^{2}=5^{2}+5^{2}\).

Step2: Calculate \(d^{2}\)

\(d^{2}=25 + 25=50\).

Step3: Solve for \(d\)

Take the square root of both sides: \(d=\sqrt{50}\).
Simplify \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\).

Answer:

\(5\) radical \(2\)