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Bot GPT 3.5 The perimeter of a triangle is found by adding up the lengths of all three sides.
Given that the width is x and the height is 4x, the base of the triangle is also x (since the width and base of a triangle are the same).
Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse^2 = base^2 + height^2
hypotenuse^2 = x^2 + (4x)^2
hypotenuse^2 = x^2 + 16x^2
hypotenuse^2 = 17x^2
hypotenuse = sqrt(17)x
The perimeter of the triangle is:
Perimeter = x + 4x + sqrt(17)x
Perimeter = 5x + sqrt(17)x
Perimeter = (5 + sqrt(17))x
So, the exact perimeter of the triangle is (5 + sqrt(17))x.