Question

Медиана прямоугольного равнобедренного треугольника, проведенная к основанию, равна 4 см.Найдите стороны данного треугольника Помогите плиз))))))) Очень надо

Answer 1

У прямоугольного равнобедренного треугольника острые углы равны по 45 градусов.
Поэтому высота из прямого угла (она же и медиана) равна половине гипотенузы.
Отсюда находим гипотенузу: она равна 2*4 = 8 см.
Катеты равны 8*cos45 = 8*(√2/2) = 4√2.

Answer 2

Finding the Sides of the Isosceles Right-Angled Triangle

To find the sides of the given isosceles right-angled triangle, we can use the fact that the median drawn to the hypotenuse of an isosceles right-angled triangle is half the length of the hypotenuse. Let's denote the length of the median as \(m\) and the length of the hypotenuse as \(h\).

Given: - Median drawn to the base = 4 cm

We can use the following steps to find the sides of the triangle:

1. Finding the Hypotenuse (h): - The median drawn to the base is half the length of the hypotenuse. - Therefore, \(m = \frac{h}{2}\). - Solving for \(h\), we get \(h = 2m\).

2. Finding the Legs (a): - In an isosceles right-angled triangle, the legs are equal. - Let's denote the length of each leg as \(a\). - Using the Pythagorean theorem, we have \(a^2 + a^2 = h^2\). - Simplifying, we get \(2a^2 = h^2\). - Substituting \(h = 2m\), we get \(2a^2 = (2m)^2\). - Solving for \(a\), we get \(a = \sqrt{2} \times m\).

Calculating the Sides

1. Hypotenuse (h): - Using the given median length, we find \(h = 2 \times 4 = 8\) cm.

2. Legs (a): - Using the calculated hypotenuse, we find \(a = \sqrt{2} \times 4 = 4\sqrt{2}\) cm.

Therefore, the sides of the given isosceles right-angled triangle are: - Hypotenuse (h): 8 cm - Legs (a): \(4\sqrt{2}\) cm

These calculations are based on the properties of isosceles right-angled triangles and the relationship between the median and the hypotenuse.