Answer:
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
Explanation:
To find the circumference of a circle circumscribed about a right triangle with legs 5 cm and 3 cm, we can use the Pythagorean theorem to find the length of the hypotenuse, which is also the diameter of the circle.
Using the Pythagorean theorem, we have:
c^2 = 5^2 + 3^2
c^2 = 25 + 9
c^2 = 34
c = sqrt(34)
So the diameter of the circle is sqrt(34) cm, and the radius is half of the diameter, or sqrt(34)/2 cm.
The circumference of a circle is given by the formula:
C = 2 * pi * r
where pi is approximately 3.14 and r is the radius of the circle.
Substituting the value of the radius, we get:
C = 2 * 3.14 * sqrt(34)/2
C = 3.14 * sqrt(34)
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).