Question

Катет прямокутного трикутника дорівнює 12 см, а медіана, проведена до іншого катета, - 13 см. Знайти гіпотенузу трикутника

Answer 1

Ответ:

∆ABC-прямокутний

<C=90° AK- медіана CK=KB

∆AKC-прямлкутний CK=√AK²-CA²=√13²-12²=√169-144=√25=5

KB=5 CB=CK+KB=5+5=10

AB²=CA²+CB²=12²+10²=144+100=244

AB=2√61

Answer 2

Finding the Hypotenuse of a Right Triangle

To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which 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 length of one of the legs (or catheti) of the right triangle as a and the length of the other leg as b. The length of the hypotenuse will be denoted as c.

In this case, we are given that one cathetus of the right triangle is 12 cm and the median drawn to the other cathetus is 13 cm. We need to find the length of the hypotenuse.

Applying the Pythagorean Theorem

According to the Pythagorean theorem, we have the following equation:

a^2 + b^2 = c^2

In our case, one cathetus is 12 cm, so we can substitute a = 12. The median drawn to the other cathetus is 13 cm, so we can substitute b = 13.

Substituting these values into the equation, we get:

12^2 + 13^2 = c^2

Simplifying the equation, we have:

144 + 169 = c^2

313 = c^2

Taking the square root of both sides, we find:

c = √313

Calculating the Hypotenuse

To calculate the length of the hypotenuse, we need to find the square root of 313. Using a calculator or a math tool, we find that the square root of 313 is approximately 17.68.

Therefore, the length of the hypotenuse of the right triangle is approximately 17.68 cm.

Please note that the calculations provided are based on the information given in the question. If there are any additional details or context, the answer may vary.

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