Question

use the square to answer the question. what is the length of a diagonal of the square? a. 30 b. 30\sqrt{2} c. 30\sqrt{3} d. 60

Explanation:

Step1: Recall Pythagorean theorem

In a square of side - length \(a\), if the side - length \(a = 30\), and the diagonal \(d\) forms the hypotenuse of a right - triangle with two sides of the square. According to the Pythagorean theorem \(d^{2}=a^{2}+a^{2}\) (since in a square, the two legs of the right - triangle formed by the diagonal have equal lengths).

Step2: Substitute the value of \(a\)

Given \(a = 30\), then \(d^{2}=30^{2}+30^{2}=900 + 900=1800\).

Step3: Solve for \(d\)

\(d=\sqrt{1800}=\sqrt{900\times2}=30\sqrt{2}\).

Answer:

B. \(30\sqrt{2}\)