Question

find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 3\sqrt{5}\) (hypotenuse) and \(a = 6\). So \(x^{2}+6^{2}=(3\sqrt{5})^{2}\).

Step2: Simplify the equation

\(x^{2}+36 = 9\times5\). Then \(x^{2}+36=45\).

Step3: Solve for \(x^{2}\)

Subtract 36 from both sides: \(x^{2}=45 - 36\). So \(x^{2}=9\).

Step4: Find \(x\)

Take the square root of both sides: \(x=\sqrt{9}\). Since \(x>0\) (length of a side), \(x = 3\).

Answer:

\(3\)