Question

Длина одного из катетов прямоугольного треугольна равно 24см, а длины второго катета и гипотенузы относятся как 5:13. Найдите длину гипотенузы.(помогите, заранее спасибо)

Answer 1

Гипотенуза=13х, а второй катет=5х.
1. По теореме Пифагора
(13х)^2=(5х)^2+24^2
169х^2-25х^2=576
144х^2=576
х^2=4
х=2
2. 13*2=26(гипотенуза)
3.5*2=10(второй катет)

P.S. если что вот этот знак ^ означает степень:)

Answer 2

Если с=13х, то а=5х и По теореме пифагора: с=√(а²+в²)⇒в=√(с²-а²), получим:
(13х)²-(5х)²=24²
169х²-25х²=576
144х²=576
х²=4
х1=-√4 - меньше ноля, не подходит по условию
х2=2(см)
с=13*2=26(см) 
☺

   

Answer 3

Finding the Length of the Hypotenuse

To find the length of the hypotenuse in 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.

In this case, we are given that one of the legs (one of the sides adjacent to the right angle) has a length of 24 cm. We are also given that the ratio of the lengths of the other leg to the hypotenuse is 5:13.

Let's denote the length of the second leg as x and the length of the hypotenuse as y. According to the given ratio, we can write:

x:y = 5:13

Using the Pythagorean theorem, we can write the equation:

x^2 + 24^2 = y^2

Now, we can solve this equation to find the length of the hypotenuse.

To solve the equation, we need to find the value of x. We can do this by rearranging the equation:

x^2 = y^2 - 24^2

x^2 = y^2 - 576

Now, we can substitute the value of x from the given ratio:

(5y/13)^2 = y^2 - 576

Simplifying the equation:

25y^2/169 = y^2 - 576

25y^2 = 169(y^2 - 576)

25y^2 = 169y^2 - 98544

144y^2 = 98544

y^2 = 98544/144

y^2 = 684

Taking the square root of both sides, we find:

y = √684

Using a calculator, we can find that the square root of 684 is approximately 26.1916.

Therefore, the length of the hypotenuse is approximately 26.1916 cm.

Please note that the calculations provided are based on the given information and assumptions.