We are given a right triangle with one leg of length 3.1 mm and a hypotenuse of length 7.1 mm. We need to find the length of the other leg, denoted as $a$, and round the answer to the nearest tenth.

1. Problem Description

We are given a right triangle with one leg of length 3.1 mm and a hypotenuse of length 7.1 mm. We need to find the length of the other leg, denoted as $a$, and round the answer to the nearest tenth.

2. Solution Steps

We will use the Pythagorean theorem to find the length of the missing leg. The Pythagorean theorem states that in a right triangle with legs of length $a$ and $b$, and a hypotenuse of length $c$, the following relationship holds:

$a^2 + b^2 = c^2$

In this problem, we are given $b = 3.1$ and $c = 7.1$. We need to find $a$. We can rearrange the Pythagorean theorem to solve for $a$:

$a^2 = c^2 - b^2$

Substituting the given values:

$a^2 = (7.1)^2 - (3.1)^2$

$a^2 = 50.41 - 9.61$

$a^2 = 40.8$

Now, we take the square root of both sides to find $a$:

$a = \sqrt{40.8}$

$a \approx 6.3874877...$

Rounding to the nearest tenth, we get:

$a \approx 6.4$

3. Final Answer

$a = 6.4$ millimeters