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.
225 + x^2= (x+1)^2
225 + x^2 = x^2 + 2 x + 1
2 x = 224
x = 112
x+1 = 113
perimeter = 15 + 112 + 113
The other sides :
x and x + 1
where x + 1 is the hypotenuse
So Pythagorean theorem:
( x + 1 )² = x² + 15²
x² + 2 x + 1 = x² + 225
Both x² get cancelled
2 x + 1 = 225
2 x = 225 - 1 = 224
x = 224 / 2 = 112 m
Hypotenuse:
x + 1 = 112 + 1 = 113 m
Perimeter = 15 +112 + 113 = 240 m
Checking the solution:
112² + 15² = 12544 + 225 = 12769 = 113²
To find the lengths of the other two sides, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the lengths of the two other sides as x and x+1 (since they are consecutive integers). According to the given information, one leg has a length of 15 m. So, we have:
15^2 + x^2 = (x+1)^2
Simplifying the equation:
225 + x^2 = x^2 + 2x + 1
Rearranging the terms:
x^2 - x^2 + 2x = 1 - 225
2x = -224
x = -112
Since lengths cannot be negative, there seems to be an error in the question. It's not possible for the other two sides to have lengths that are consecutive integers.
Please double-check the information provided and make sure it is correct.