Question

find d.
write your answer in simplest radical form.
units

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so legs are equal, hypotenuse is \( leg \times \sqrt{2} \). Here, hypotenuse is \( \sqrt{6} \), let leg be \( d \).

Step2: Use 45-45-90 ratio

In 45-45-90, \( hypotenuse = d\sqrt{2} \). So \( d\sqrt{2} = \sqrt{6} \).

Step3: Solve for \( d \)

Divide both sides by \( \sqrt{2} \): \( d = \frac{\sqrt{6}}{\sqrt{2}} \). Rationalize: \( d = \sqrt{\frac{6}{2}} = \sqrt{3} \).

Answer:

\(\sqrt{3}\)