Question

Медіана прямокутного трикутника яка проведена до гіпотенузи дорівнює 13 , 6 сантиметрів знайдіть гіпотенузу прямокутного трикутника

Answer 1

Медиана прямоугольного треугольника , проведённая к гипотенузе  равна половине гипотенузы . Значит гипотенуза в два раза больше этой медианы и равна  13,6 * 2 = 27,2 см .

Answer 2

Ответ: 27,2

Объяснение: Коли трикутнiк ABC з прямим кутом A та медiаною AD, ця медiана рiвна половiнi гiпотенузы: AD = BD = CD

Answer 3

Finding the Hypotenuse of a Right Triangle

To find the length of 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 other two sides.

Let's denote the lengths of the two legs of the right triangle as a and b, and the length of the hypotenuse as c. According to the Pythagorean theorem, we have the equation:

a^2 + b^2 = c^2

In this case, we are given that a median is drawn to the hypotenuse of the right triangle, and its length is 13 and 6 centimeters. However, it is not clear which side the median is drawn from. To solve this problem, we need to make an assumption.

Assumption: The median is drawn from one of the legs of the right triangle.

Let's assume that the median is drawn from the leg with length a. Therefore, we have the following information:

Length of the median = 13 cm Length of the other leg = 6 cm

We can use this information to find the length of the hypotenuse c.

Solution

To find the length of the hypotenuse, we can use the Pythagorean theorem. Since the median is drawn from the leg with length a, we can write the equation as:

a^2 = c^2 - b^2

Substituting the given values, we have:

a^2 = c^2 - 6^2

Simplifying further, we get:

a^2 = c^2 - 36

Since we know that the length of the median is 13 cm, we can write another equation:

a = 13

Substituting this value into the previous equation, we have:

13^2 = c^2 - 36

Simplifying further, we get:

169 = c^2 - 36

Adding 36 to both sides of the equation, we have:

205 = c^2

Taking the square root of both sides, we get:

c = √205

Therefore, the length of the hypotenuse of the right triangle is approximately √205 centimeters.

Please note that this solution assumes that the median is drawn from the leg with length a. If the median is drawn from the other leg, the solution will be different.

I hope this helps! Let me know if you have any further questions.