Question

question 15 of 25 what is the length of the diagonal of the square shown below? a. 25 b. 5√5 c. √10 d. 5√2 e. 5 f. √5

Explanation:

Step1: Apply Pythagorean theorem

In a square with side - length \(a = 5\), the diagonal \(d\) forms a right - triangle with two sides of the square. The Pythagorean theorem is \(d^{2}=a^{2}+a^{2}\).
Since \(a = 5\), we have \(d^{2}=5^{2}+5^{2}\).

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:

D. \(5\sqrt{2}\)