Question

4 - 2 and 4 - 3 practice online
geometry (s1 p01 rm h218) sharp, jeffrey / unit 4 - right triangle trigonometry / lesson 4 - 3 half an e

1. refer to the figure.

what is the length of the diagonal?
units (give an exact answer)

Explanation:

Step1: Identify the side length of the square

From the figure, the side length of the square \(a = 1\) unit.

Step2: Use the Pythagorean theorem for the square's diagonal

In a square, if the side length is \(a\) and the diagonal is \(d\), by the Pythagorean theorem \(d^{2}=a^{2}+a^{2}\). Substituting \(a = 1\), we get \(d^{2}=1^{2}+1^{2}=1 + 1=2\).

Step3: Solve for \(d\)

Taking the square root of both sides, \(d=\sqrt{2}\) (since \(d>0\) as it represents a length).

Answer:

\(\sqrt{2}\)