Question

Катеты прямоугольного треугольника равны 12 и 5 найдите диаметр окружности описанной около него

Answer 1

По теореме Пифагора находим гипотенузу треугольника по формуле:c^2=a^2+b^2(^2 значит в квадрате,это в тетради не писать!)
Подставляем значения катетов,получаем:
c^2=12^2+5^2=144+25=169, следовательно c,т.е. гипотенуза=под корнем 169=13.
Диаметр окружности описанной около прямоугольного треугольника это гипотенуза этого треугольника.Задача решена.
Ответ:13

Answer 2

Finding the Diameter of the Circumscribed Circle

To find the diameter of the circumscribed circle of a right triangle with legs measuring 12 and 5, we can use the properties of right triangles and the relationship between the diameter and the hypotenuse of the circumscribed circle.

Let's break down the solution step by step:

1. The legs of the right triangle are given as 12 and 5. 2. The hypotenuse of the right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. - Applying the Pythagorean theorem, we have: hypotenuse^2 = 12^2 + 5^2. - Simplifying the equation, we get: hypotenuse^2 = 144 + 25. - Calculating the sum, we find: hypotenuse^2 = 169. - Taking the square root of both sides, we get: hypotenuse = 13. 3. The diameter of the circumscribed circle is equal to the hypotenuse of the right triangle. - Therefore, the diameter of the circumscribed circle is 13.

So, the diameter of the circumscribed circle of the right triangle with legs measuring 12 and 5 is 13.

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