We are given a right triangle with hypotenuse 25 mm and one leg 24 mm. We need to find the length of the other leg, which is labeled as $a$.

1. Problem Description

We are given a right triangle with hypotenuse 25 mm and one leg 24 mm. We need to find the length of the other leg, which is labeled as $a$.

2. Solution Steps

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

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

In this problem, we have $b = 24$ mm and $c = 25$ mm. We want to find $a$. Plugging in the given values, we have:

$a^2 + (24)^2 = (25)^2$

$a^2 + 576 = 625$

Subtract 576 from both sides:

$a^2 = 625 - 576$

$a^2 = 49$

Take the square root of both sides:

$a = \sqrt{49}$

$a = 7$

3. Final Answer

The length of the missing leg is 7 mm.