Question

Пожалуйста!Срочно! Катеты прямоугольного треугольника относиться как 5:12,а его гипотенуза=13см. Найдите периметр треугольника. С объяснениями пожалуйста.

Answer 1

Ответ:

12 см.

Объяснение:

Назовем треугольник АВС. ВС - по условию гипотенуза, равная 13 см. Известно, что катеты относятся, как 5:12, тогда, АС = 5х (см), а АВ = 12 х (см). ( Условно разделив катеты на части, получаем, что 1 часть = х см). По теореме Пифагора: ВC в кв. = АС в кв. + АВ в кв. Составим и решим уравнение. 13 в кв. = 12х в кв. + 5х в кв; 169 = 144х в кв. + 25х в кв; 169 = 169х в кв. х в кв. = корень квадратный из 169:169; х = 1.

Итак, АС= 5х1=5 (см); АВ = 12х1=12 (см)

Answer 2

Given Information:

We are given that the ratios of the two legs of a right triangle are 5:12, and the length of the hypotenuse is 13 cm.

Solution:

To find the perimeter of the triangle, we need to find the lengths of the two legs and then add them to the length of the hypotenuse.

Let's assume the lengths of the two legs are 5x and 12x, where x is a common factor. According to the given ratio, we have:

Length of the first leg = 5x Length of the second leg = 12x

We can use the Pythagorean theorem to find the value of x. 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.

Using the given information, we have:

(5x)^2 + (12x)^2 = 13^2

Simplifying the equation:

25x^2 + 144x^2 = 169

169x^2 = 169

Dividing both sides by 169:

x^2 = 1

Taking the square root of both sides:

x = 1

Now that we have the value of x, we can find the lengths of the two legs:

Length of the first leg = 5x = 5 * 1 = 5 cm Length of the second leg = 12x = 12 * 1 = 12 cm

Finally, we can calculate the perimeter of the triangle by adding the lengths of the two legs and the hypotenuse:

Perimeter = Length of the first leg + Length of the second leg + Length of the hypotenuse Perimeter = 5 cm + 12 cm + 13 cm Perimeter = 30 cm

Therefore, the perimeter of the triangle is 30 cm.

Explanation:

In a right triangle, the two legs are the sides that form the right angle, and the hypotenuse is the side opposite the right angle. The Pythagorean theorem states that 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, we are given the ratio of the two legs as 5:12 and the length of the hypotenuse as 13 cm. By assuming the lengths of the two legs as 5x and 12x, we can use the Pythagorean theorem to find the value of x. Solving the equation, we find that x = 1.

Substituting the value of x back into the expressions for the lengths of the two legs, we find that the lengths of the legs are 5 cm and 12 cm.

Finally, we calculate the perimeter of the triangle by adding the lengths of the two legs and the hypotenuse. The perimeter is found to be 30 cm.