Question

solve for w. do not convert your answer to decimal form and rationalize the denominator if necessary.
show your work here
hint: to add the square root symbol (√□), type
oot\

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\). Let the legs be \(a\) (here \(a = 17\)) and the hypotenuse be \(w\). The formula for the hypotenuse \(w\) of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle is \(w=a\sqrt{2}\).

Step2: Substitute the value of \(a\)

Substitute \(a = 17\) into the formula \(w=a\sqrt{2}\). So \(w = 17\sqrt{2}\).

Answer:

\(17\sqrt{2}\)