Question

determine the missing length(s) in each triangle. write your answer as a radical in simplest form.
2 in.
2 in.
enter the answer in the space provided. use numbers instead of words.
inches

Explanation:

Step1: Identify the formula

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 2\), \(b = 2\), and \(c\) is the hypotenuse.

Step2: Substitute the values

Substitute \(a = 2\) and \(b = 2\) into the formula: \(2^2 + 2^2 = c^2\).

Step3: Calculate the squares

\(4 + 4 = c^2\), so \(8 = c^2\).

Step4: Solve for \(c\)

Take the square root of both sides: \(c = \sqrt{8}\). Simplify \(\sqrt{8}\) to \(2\sqrt{2}\).

Answer:

\(2\sqrt{2}\)