Answer:
Explanation:
Let's assume that the hypotenuse of the right triangle has a length of x.
According to the problem statement, the shorter leg is 8 less than the hypotenuse, so its length is x - 8.
Similarly, the longer leg is 1 less than the hypotenuse, so its length is x - 1.
We can now use the Pythagorean theorem to write an equation that relates the lengths of the three sides:
(x - 8)^2 + (x - 1)^2 = x^2
Expanding and simplifying this equation, we get:
2x^2 - 18x + 65 = 0
Solving for x using the quadratic formula, we get:
x = (18 ± √244) / 4
We can discard the negative solution, as x represents the length of the hypotenuse, which must be positive. So we have:
x = (18 + √244) / 4 ≈ 6.12
Now we can calculate the lengths of the other two sides:
Shorter leg: x - 8 ≈ -1.88 (discard, as it is negative)
Longer leg: x - 1 ≈ 5.12
The perimeter of the triangle is the sum of the lengths of the three sides:
Perimeter = x + (x - 1) + (x - 8) = 3x - 9
Substituting x ≈ 6.12, we get:
Perimeter ≈ 3(6.12) - 9 ≈ 9.36
Therefore, the perimeter of the right triangle is approximately 9.36.