Question

for c. do not convert your answer to decimal form and rationalize t ssary.
draw
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 \(a = b=17\). The formula for the hypotenuse \(c\) of a right - triangle is \(c=\sqrt{a^{2}+b^{2}}\) (by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\)).

Step2: Substitute the values of \(a\) and \(b\)

Since \(a = 17\) and \(b = 17\), we have \(c=\sqrt{17^{2}+17^{2}}\). Simplify the expression inside the square root: \(17^{2}+17^{2}=2\times17^{2}\). So \(c=\sqrt{2\times17^{2}}\).

Step3: Simplify the square - root

Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 2\), \(b = 17^{2}\)), we get \(c = 17\sqrt{2}\).

Answer:

\(17\sqrt{2}\)