Question

Катеты прямоугольного треугольника относятся,как 3:4,а его гипотенуза равна 10 см найти катеты треугольника.

Answer 1

Отметим катеты как 3х и 4х. Значит 3 x^{2}+4x^{2}= 10^{2} 
9x^{2} +16x^{2}=100   25x^{2}=100   x^{2} = 100:25 
x^{2}= 4
х= \sqrt{4} = 2
Первый катет = 3*2=6
второй катет= 4*2=8 
ответ: 3 см, 4 см.

Answer 2

Finding the Length of the Catheti of a Right Triangle

To find the lengths of the catheti of a right triangle when the ratio between them is given, we can use the following steps:

1. Identify the given information: - The ratio between the catheti is 3:4. - The length of the hypotenuse is 10 cm.

2. Set up the equation: - Let's assume the lengths of the catheti are 3x and 4x, where x is a scaling factor. - According to the given ratio, we have the equation: 3x + 4x = 10.

3. Solve the equation: - Combine like terms: 7x = 10. - Divide both sides of the equation by 7: x = 10/7.

4. Calculate the lengths of the catheti: - Substitute the value of x back into the equation: - Length of the first cathetus: 3x = 3 * (10/7) = 30/7 cm. - Length of the second cathetus: 4x = 4 * (10/7) = 40/7 cm.

Therefore, the lengths of the catheti of the right triangle are 30/7 cm and 40/7 cm.

Please note that the lengths of the catheti are given as fractions, which are the exact values. If you prefer decimal approximations, you can calculate them by dividing the numerator by the denominator.

Let me know if there's anything else I can help you with!