Question

for c. do not convert your answer to decimal form and rationaliz ssary. work here d the square root symbol (√□), type
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Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal. Let the legs be \(a = 5\) and \(b = 5\) (since the non - hypotenuse sides of a 45 - 45 - 90 triangle are congruent).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Substitute \(a = 5\) and \(b = 5\) into the formula:

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Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{50}\). Simplify \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\)

Answer:

\(5\sqrt{2}\)