Question

1. refer to the figure,

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

Explanation:

Step1: Determine the side length of the square

The side length of the square is \(4 + 1=5\) units.

Step2: Apply the Pythagorean theorem

For a square with side length \(a\), the length of the diagonal \(d\) is given by \(d=\sqrt{a^{2}+a^{2}}\) (since in a square, the two sides forming the right - angle for the diagonal are equal). Substituting \(a = 5\), we get \(d=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}\). Simplify \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\).

Answer:

\(5\sqrt{2}\)