Question

ТЕРМІНОВО, 70 БАЛІВ гіпотенуза і катет прямокутного трикутника відносяться як 5: 4. а другий катет дорівнює 12 см. знайдіть радіус кола, описаного навколо трикутника

Answer 1

Ответ:

10

Объяснение:

є такі прямокутні трикутники, де катети = 3 і 4, а гіпотенуза = 5 або кратні їм

у нас один катет = 12 (кратний трьом), отже, другий катет = 4×4 = 16, а гіпотенуза = 5×4 = 20

центр описаного навколо прямокутного трикутника кола лежить на середині гіпотенузи

радіус = 20/2 = 10

Answer 2

Problem Analysis

To find the radius of the circle circumscribed around a right triangle, we need to use the relationship between the hypotenuse and one of the legs of the triangle. In this case, we are given that the ratio of the hypotenuse to one of the legs is 5:4. We are also given the length of the second leg, which is 12 cm.

Solution

Let's denote the length of the hypotenuse as h, the length of the first leg as a, and the length of the second leg as b.

According to the given information, we have the following relationship: h:a = 5:4

We are also given that b = 12 cm.

To find the radius of the circle circumscribed around the triangle, we can use the formula: radius = (h + a + b) / 2

Calculation

To find the value of a, we can use the given ratio: h:a = 5:4

Cross-multiplying, we get: 4h = 5a

Simplifying, we find: a = (4/5)h

Substituting this value of a into the formula for the radius, we have: radius = (h + (4/5)h + 12) / 2

Simplifying further, we get: radius = (9/5)h + 12 / 2 radius = (9/5)h + 6

Answer

Therefore, the radius of the circle circumscribed around the triangle is (9/5)h + 6.

Please note that we need the value of h to calculate the exact radius. If you have the value of h, you can substitute it into the formula to find the radius.