Question

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

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 \(a = b=15\), and the hypotenuse \(m\).

Step2: Use the 45 - 45 - 90 triangle formula

The formula for the hypotenuse \(m\) of a 45 - 45 - 90 triangle is \(m = a\sqrt{2}\) (where \(a\) is the length of a leg). Substitute \(a = 15\) into the formula: \(m=15\sqrt{2}\).

Answer:

\(m = 15\sqrt{2}\)