Answer:
14.2 km
Step-by-step explanation:
You want the perimeter of a right triangle with hypotenuse 6 km and one leg 3 km.
Special triangle
We recognize the right triangle with one leg half the hypotenuse as being the 30°-60°-90° "special" right triangle that has sides in the ratios ...
1 : √3 : 2
The sum of these side lengths is 1+√3+2 = 3+√3.
Your triangle has a shortest side that is 3 km, so this perimeter value must be multiplied by 3 km to give the perimeter of your triangle:
(3 km)(3 +√3) ≈ 14.2 km
The perimeter of the right triangle is about 14.2 km.
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Additional comment
You can find the other leg from the Pythagorean theorem:
a = √(c² -b²) = √(6² -3²) = √27 = 3√3 ≈ 5.2
P = a+b+c = 5.2 +3 +6 = 14.2 . . . . km
The other "special" right triangle is the 45°-45°-90° isosceles right triangle. It has sides in the ratios 1 : 1 : √2.
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