Question

Знайдіть менший катет прямокутного трикутника та його висоту проведену до гіпотенузи, якщо більший катет менший на 10 см і більший за свою проекцію на гіпотенузу на 8 см​

Answer 1

Відповідь:
Розв’язання на фото

Answer 2

To find the smaller leg of a right triangle and its height drawn to the hypotenuse, we can use the Pythagorean theorem and the concept of similar triangles.

Let's denote the smaller leg of the triangle as 'x' and the larger leg as 'x + 10'. The projection of the larger leg onto the hypotenuse is 'x + 8'.

Using the Pythagorean theorem, we can set up the following equation:

x^2 + (x + 10)^2 = (x + 8)^2

Simplifying this equation will allow us to solve for 'x'.

Expanding the equation:

x^2 + (x^2 + 20x + 100) = (x^2 + 16x + 64)

Combining like terms:

2x^2 + 20x + 100 = x^2 + 16x + 64

Rearranging the equation:

x^2 + 4x + 36 = 0

Now, we can solve this quadratic equation to find the value of 'x'.