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Find the exact perimeter of the triangle.%0D%0A%0D%0A%0D%0A%0D%0A(1 point)
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
2 months ago
![COWBOYS](/images/users/0/1/128x128.jpeg)
2 months ago
4x on a leg, x on the other leg, and nothing for the hypotenuse
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
2 months ago
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.