Question

Площадь прямоугольного треугольника 42см один из катетов составляет 84% второго найти длину катетов

Answer 1

Пусть один катет х см, тогда второй будет 0,84 х см.
По формуле площади составим уравнение.
1/2•х•0,84х=42
42/100 х^2=42
х^2=42:42/100
х^2=100
х=10 см первый катет
10•0,84=8,4 см второй катет

Answer 2

Calculation of the Length of the Legs of a Right Triangle

To find the lengths of the legs of a right triangle, we can use the given information about the area and the ratio between the lengths of the legs.

Let's denote the lengths of the legs as x and y. According to the given information, the area of the triangle is 42 square centimeters, and one of the legs is 84% of the length of the other leg.

The formula for the area of a right triangle is:

Area = (1/2) * base * height

In this case, the base and height are the lengths of the legs. So we have:

42 = (1/2) * x * y

We also know that one of the legs is 84% of the length of the other leg. Mathematically, this can be expressed as:

x = 0.84 * y

Now we can solve these equations to find the lengths of the legs.

Solution:

Substituting the value of x from the second equation into the first equation, we get:

42 = (1/2) * (0.84 * y) * y

Simplifying the equation, we have:

42 = (0.42) * y^2

Dividing both sides of the equation by 0.42, we get:

y^2 = 100

Taking the square root of both sides, we find:

y = 10

Substituting this value of y back into the second equation, we can find the value of x:

x = 0.84 * 10 = 8.4

Therefore, the lengths of the legs of the right triangle are x = 8.4 cm and y = 10 cm.

Please note that the above solution assumes that the given information is accurate and that the triangle is a right triangle.