One leg of a right triangle has a length of 15 m. The other sides have lengths that are consecutive integers. Find the number of meters in the perimeter.

x^2+15^2 = (x+1)^2

x = 112

p = 15+112+113

To solve this problem, we can use the Pythagorean theorem, which states that in any 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 other two sides.

Let's call the two consecutive integer side lengths x and (x+1).
According to the problem, one leg has a length of 15 m.

Using the Pythagorean theorem, we can set up the following equation:
15^2 + x^2 = (x+1)^2

Simplifying this equation, we get:
225 + x^2 = x^2 + 2x + 1

The x^2 terms cancel out, leaving us with:
225 = 2x + 1

Subtracting 1 from both sides, we get:
224 = 2x

Dividing both sides by 2, we find:
112 = x

So, one of the consecutive integer side lengths is 112 meters, and the other side length is (112+1) = 113 meters.

To find the perimeter of the right triangle, we need to add up the lengths of all three sides.

Perimeter = 15 + 112 + 113 = 240 meters

Therefore, the number of meters in the perimeter is 240.