Question

Найдите медиану, проведенную к гипотенузе прямоугольного треугольника, если катеты равны 60 см и 11 см. (Знайдіть медіану, проведену до гіпотенузи прямокутного трикутника, якщо катети дорівнюють 60 см і 11 см.)

Answer 1

Медиана= 1/2 Va^2+b^2=0,5*V3600+121= 0,5*61= 30,5

Answer 2

1) Корень из  3600 + 121 = Корень из3721 = 61

2) В прямоугольном треугольнике, медиана, проведённая к гипотенузе равна половине этой гипотенузы, значит медиана равна 61:2=30,5

Ответ: 30,5

Answer 3

To find the median drawn to the hypotenuse of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the lengths of the legs (or catheti) are given as 60 cm and 11 cm. Let's denote the length of the hypotenuse as c.

Using the Pythagorean theorem, we can write the equation as:

c^2 = 60^2 + 11^2

Simplifying the equation:

c^2 = 3600 + 121

c^2 = 3721

Taking the square root of both sides:

c = √3721

c ≈ 61

Therefore, the length of the hypotenuse is approximately 61 cm.

Now, to find the median drawn to the hypotenuse, we can use the fact that the median of a right triangle is half the length of the hypotenuse. So, the median would be:

Median = 1/2 * hypotenuse

Substituting the value of the hypotenuse:

Median ≈ 1/2 * 61

Median ≈ 30.5 cm

Therefore, the median drawn to the hypotenuse of the right triangle with legs measuring 60 cm and 11 cm is approximately 30.5 cm.