Question

1. 2 yd, 3 yd, √13 yd

Explanation:

Assuming the problem is to determine if these side lengths form a right triangle (using the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the longest side).

Step 1: Identify the longest side

The sides are \(2\) yd, \(3\) yd, \(\sqrt{13}\) yd. The longest side is \(\sqrt{13}\) yd since \(\sqrt{13}\approx3.605>3>2\).

Step 2: Calculate \(a^2 + b^2\) (where \(a = 2\), \(b = 3\))

\(a^2 + b^2=2^2 + 3^2 = 4 + 9 = 13\)

Step 3: Calculate \(c^2\) (where \(c=\sqrt{13}\))

\(c^2 = (\sqrt{13})^2 = 13\)

Step 4: Compare \(a^2 + b^2\) and \(c^2\)

Since \(a^2 + b^2 = 13\) and \(c^2 = 13\), we have \(a^2 + b^2 = c^2\).

Answer:

These side lengths form a right triangle (by the Pythagorean theorem).