Question

abcd is a square. bc = 8. find the length of the diagonal \overline{ac}
a
b
8
d
c
16
8\sqrt{2}
16\sqrt{2}
8

Explanation:

Step1: Identify the properties of a square

In square \(ABCD\), \(AB = BC=CD = DA = 8\) and \(\angle B=90^{\circ}\) (property of a square).

Step2: Apply the Pythagorean theorem

In right - triangle \(ABC\), by the Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). Since \(AB = BC = 8\), we have \(AC^{2}=8^{2}+8^{2}\).

$$
LATEXBLOCK0
$$

Answer:

\(8\sqrt{2}\) (the second option)