Question

a 45°-45°-90° triangles leg has a length of $3\sqrt{2}$ inches. what is the length of the hypotenuse? write your answer in simplest radical form. inches

Explanation:

Step1: Recall the ratio in a 45°-45°-90° triangle

In a 45°-45°-90° triangle, the ratio of the length of a leg to the length of the hypotenuse is \(1:\sqrt{2}\). That is, if the length of a leg is \(l\), the length of the hypotenuse \(h\) is \(l\times\sqrt{2}\).

Step2: Substitute the given leg length into the formula

The given leg length \(l = 3\sqrt{2}\) inches. Substituting into the formula \(h=l\times\sqrt{2}\), we get \(h = 3\sqrt{2}\times\sqrt{2}\).

Step3: Simplify the expression

Using the property of radicals \(\sqrt{a}\times\sqrt{a}=a\) (for \(a\geq0\)), we have \(\sqrt{2}\times\sqrt{2} = 2\). So \(h=3\times2=6\).

Answer:

6