To make a rectangular table more stable, a diagonal brace is attached to the underside of the table surface. If the table is $15 \mathrm{dm}$ by $20 \mathrm{dm}$, how long is the brace?

The length of the brace is $\square \mathrm{dm}$.

Step 1 ：The problem is asking for the length of the diagonal brace attached to the underside of a rectangular table. The dimensions of the table are given as 15 dm by 20 dm.

Step 2 ：We can use the Pythagorean theorem to solve this problem. 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. This can be written as: \(a² + b² = c²\).

Step 3 ：In this case, the sides of the rectangle are the two sides of the right triangle and the brace is the hypotenuse. So, we can calculate the length of the brace using this formula.

Step 4 ：Let's substitute the given values into the formula. Here, \(a = 15\) and \(b = 20\).

Step 5 ：So, \(c² = a² + b² = 15² + 20² = 225 + 400 = 625\).

Step 6 ：To find the length of the brace (c), we take the square root of 625, which gives us \(c = 25.0\).

Step 7 ：Final Answer: The length of the brace is \(\boxed{25 \mathrm{dm}}\).