Question

find the length of side x in simplest radical form with a rational denominator.
answer
x - submit answer

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length and the hypotenuse \(c\) is related to a leg \(a\) by the formula \(c = a\sqrt{2}\). Here, one of the legs \(a = 4\).

Step2: Apply the 45 - 45 - 90 triangle formula

Using the formula \(x=a\sqrt{2}\) (where \(x\) is the hypotenuse and \(a\) is the leg). Substitute \(a = 4\) into the formula: \(x=4\sqrt{2}\). The denominator is already rational (since there is no radical in the denominator in the form \(\frac{\text{expression}}{\text{radical}}\)).

Answer:

\(4\sqrt{2}\)