Calculate the hypotenuse of a right triangle with two legs of length 1/4 ft.

1. Identify the problem type: The image shows a right triangle with the lengths of the two legs given. This is a geometry problem that can be solved using the Pythagorean theorem.

1. Recall the Pythagorean theorem: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). Mathematically, this is expressed as $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.

1. Assign values to the variables: From the image, we can see that the lengths of the two legs are $a = \frac{1}{4}$ ft and $b = \frac{1}{4}$ ft.

4. Substitute the values into the Pythagorean theorem:
$$ \left(\frac{1}{4}\right)^2 + \left(\frac{1}{4}\right)^2 = c^2 $$

5. Calculate the squares of the legs:
$$ \frac{1}{16} + \frac{1}{16} = c^2 $$

6. Add the squares of the legs:
$$ \frac{2}{16} = c^2 $$

7. Simplify the fraction:
$$ \frac{1}{8} = c^2 $$

8. Solve for the hypotenuse (c) by taking the square root of both sides:
$$ c = \sqrt{\frac{1}{8}} $$

9. Simplify the square root (optional but good practice):
$$ c = \frac{\sqrt{1}}{\sqrt{8}} = \frac{1}{\sqrt{4 \times 2}} = \frac{1}{2\sqrt{2}} $$
To rationalize the denominator, multiply the numerator and denominator by $\sqrt{2}$: $$ c = \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2 \times 2} = \frac{\sqrt{2}}{4} $$ However, the problem does not specify the format, so $\sqrt{\frac{1}{8}}$ ft is also a valid answer. We will use the simplified form $\sqrt{\frac{1}{8}}$ ft for the final answer as it directly comes from the calculation.