Find the exact perimeter of the triangle.%0D%0A%0D%0A%0D%0A%0D%0A(1 point)
In order to find the exact perimeter of the triangle, we need to know the lengths of all three sides of the triangle. Without that information, it is not possible to calculate the exact perimeter.
4x on a leg, x on the other leg, and nothing for the hypotenuse
Given the information provided, we have:
- One leg of the triangle = 4x
- Other leg of the triangle = x
- Hypotenuse of the triangle = ?
To find the exact perimeter of the triangle, we need to first determine the length of the hypotenuse using the Pythagorean theorem. In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
So, solving for the hypotenuse:
(4x)^2 + x^2 = Hypotenuse^2
16x^2 + x^2 = Hypotenuse^2
17x^2 = Hypotenuse^2
Hypotenuse = sqrt(17x^2)
Hypotenuse = sqrt(17)*x
The perimeter of the triangle is the sum of the lengths of all three sides:
Perimeter = 4x + x + sqrt(17)*x
Perimeter = 5x + sqrt(17)*x
Therefore, the exact perimeter of the triangle is 5x + sqrt(17)*x.