A right triangle and two of its side lengths are shown in the diagram 3.7ft and 14.3ft. Which measurement is closest to the value of x in feet?

To solve this problem, we can use the Pythagorean theorem, which states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \):

\[
a^2 + b^2 = c^2
\]

As you mentioned two sides of the triangle with lengths 3.7 ft and 14.3 ft, we need to know which of these represents the legs of the triangle and which one represents the hypotenuse.

If 3.7 ft and 14.3 ft are both legs of the triangle, then the hypotenuse \( x \) can be calculated as follows:

1. \( a = 3.7 \)
2. \( b = 14.3 \)

Using the Pythagorean theorem:

\[
x^2 = 3.7^2 + 14.3^2
\]

Calculating the squares:

\[
3.7^2 = 13.69
\]
\[
14.3^2 = 204.49
\]

Now add them together:

\[
x^2 = 13.69 + 204.49 = 218.18
\]

Now take the square root to find \( x \):

\[
x = \sqrt{218.18} \approx 14.77 \text{ ft}
\]

If 14.3 ft is the hypotenuse and 3.7 ft is one of the legs, then you would set it up as:

\[
14.3^2 = 3.7^2 + x^2
\]

Calculating:

\[
14.3^2 = 204.49
\]
\[
3.7^2 = 13.69
\]

Substituting in:

\[
204.49 = 13.69 + x^2
\]

Subtract \( 13.69 \) from both sides:

\[
x^2 = 204.49 - 13.69 = 190.8
\]

Now take the square root:

\[
x = \sqrt{190.8} \approx 13.82 \text{ ft}
\]

### Conclusion
Depending on whether 3.7 ft and 14.3 ft are both legs or if one is the hypotenuse, the approximate values for \( x \) would be:

- If both are legs: \( x \approx 14.77 \) ft
- If 14.3 ft is the hypotenuse: \( x \approx 13.82 \) ft

Please clarify which sides are the legs and which is the hypotenuse for the exact answer.