Question

Бісектриса прямокутного трикутника ділить гіпатенузу на відрізки різниця яких сладає 5см. знайдіть сторони трикутника , якщо відношення катетів дорівнює 3:4.​

Answer 1

Відповідь:

ответ на фото.

Answer 2

Bisector of a Right Triangle

The bisector of a right triangle is a line segment that divides the hypotenuse into two segments. Let's denote the lengths of these two segments as x and y. According to the given information, the difference between these two segments is 5 cm.

To find the sides of the triangle, we need to determine the lengths of the other two sides, which are the legs of the right triangle. The given information also states that the ratio of the legs is 3:4.

Let's solve this problem step by step.

Step 1: Understanding the Problem

We have a right triangle with a bisector that divides the hypotenuse into two segments, x and y. The difference between these two segments is 5 cm. The ratio of the legs of the triangle is 3:4.

Step 2: Applying the Bisector Theorem

According to the Bisector Theorem, if a line segment divides a side of a triangle into two segments, then the ratio of the lengths of those segments is equal to the ratio of the lengths of the other two sides.

In our case, the bisector divides the hypotenuse into two segments, x and y. The ratio of the lengths of the legs is given as 3:4. Therefore, we can set up the following equation:

x/y = 3/4

Step 3: Finding the Lengths of x and y

To find the lengths of x and y, we need to solve the equation x/y = 3/4. We can do this by cross-multiplying:

4x = 3y

Now, we know that the difference between x and y is 5 cm. Therefore, we can set up another equation:

x - y = 5

Step 4: Solving the Equations

We have two equations:

4x = 3y (Equation 1) x - y = 5 (Equation 2)

We can solve these equations simultaneously to find the values of x and y.

Let's solve Equation 2 for x:

x = y + 5

Substituting this value of x into Equation 1:

4(y + 5) = 3y

Simplifying the equation:

4y + 20 = 3y

Subtracting 3y from both sides:

y + 20 = 0

Subtracting 20 from both sides:

y = -20

Since the length of a side cannot be negative, this solution is not valid.

Conclusion

Based on the given information, it seems that there might be an error in the problem statement or the given values. The solution obtained does not yield valid lengths for the sides of the triangle.

Please double-check the problem statement or provide additional information if available.