Question

У рівнобедрений прямокутний трикутник, кожний катет якого дорівнює 2,7 дм, вписано квадрат, що має з ним спільний кут. Знайдіть периметр квадрата. СРОЧНОООО50 ДАМ 100 БАЛОВ ПЖЖ ОЧЕНЬ НАДОООО РАСПЕШИТЕ ПЖ КАК В ШКОЛЕ​

Answer 1

У квадрата, вписанного в равнобедренный прямоугольный треугольник диагональ совпадает с биссектрисой прямого угла треугольника.

Точка пересечения биссектрисы с гипотенузой образует вершину вписанного квадрата.

А так как эта биссектриса совпадает с медианой, то полученная вершина лежит на средней линии треугольника.

Сторона квадрата равна средней линии треугольника, то есть 2,7/2 = 1,35 дм.

Ответ: периметр квадрата Р = 4*1,35 = 5,4 дм.

Answer 2

To find the perimeter of the square inscribed in an isosceles right triangle, we need to determine the length of one side of the square.

Given that each leg of the right triangle is 2.7 dm, we can use the Pythagorean theorem to find the length of the hypotenuse (the side opposite the right angle). The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's calculate the length of the hypotenuse:

Using the Pythagorean theorem: c^2 = a^2 + b^2 where c is the length of the hypotenuse, and a and b are the lengths of the legs.

In this case, a = b = 2.7 dm. Substituting the values into the equation: c^2 = 2.7^2 + 2.7^2

Calculating: c^2 = 7.29 + 7.29 c^2 = 14.58 c ≈ √14.58 c ≈ 3.82 dm

Now that we know the length of the hypotenuse, we can determine the side length of the inscribed square. In an isosceles right triangle, the hypotenuse is equal to the product of the leg length and the square root of 2.

Let's calculate the side length of the square:

s = a * √2 where s is the side length of the square, and a is the length of the leg.

In this case, a = 2.7 dm. Substituting the value into the equation: s = 2.7 * √2

Calculating: s ≈ 2.7 * 1.414 s ≈ 3.82 dm

Therefore, the side length of the square is approximately 3.82 dm.

To find the perimeter of the square, we multiply the side length by 4 (since all sides of a square are equal):

Perimeter = 4 * s Perimeter = 4 * 3.82 Perimeter ≈ 15.28 dm

Therefore, the perimeter of the square inscribed in the isosceles right triangle is approximately 15.28 dm.

Please note that the calculations are approximate due to rounding.