Question

В 1 прямоугольного один из катетов на 2 см меньшн гипотенузы а 2 катет 4 см Найти пириметер треугольника

Answer 1

Пусть гипотенуза равна х

$(x-2)^{2} +(x-4)^{2}=x^{2} \\x^{2} -4x+4+x^{2} -8x+16=x^{2} \\x^{2} -12x+20=0\\D=144-80=64\\x_{1} =\frac{12+8}{2}=10\\x_{2} =\frac{12-8}{2}=2$

x=2 не удовлетворяет условиям задачи, значит гипотенуза = 10см, один из катетов 10-2=8 см, второй 10-4=6 см

Р = 10 + 8 + 6 = 24

Answer 2

Problem Analysis

We are given a right triangle with one of the legs measuring 2 cm less than the hypotenuse and the other leg measuring 4 cm. We need to find the perimeter of the triangle.

Solution

Let's denote the hypotenuse as c, the shorter leg as a, and the longer leg as b.

From the given information, we can write the following equations: 1. a = c - 2 (one of the legs is 2 cm less than the hypotenuse) 2. b = 4 (the other leg is 4 cm)

To find the perimeter of the triangle, we need to add up the lengths of all three sides: Perimeter = a + b + c

To solve for c, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: c^2 = a^2 + b^2

Substituting the values of a and b from the given information, we get: c^2 = (c - 2)^2 + 4^2

Simplifying the equation: c^2 = c^2 - 4c + 4 + 16 0 = -4c + 20 4c = 20 c = 5

Now that we have the value of c, we can substitute it back into the equation for a to find its value: a = c - 2 = 5 - 2 = 3

Finally, we can calculate the perimeter of the triangle: Perimeter = a + b + c = 3 + 4 + 5 = 12 cm

Therefore, the perimeter of the triangle is 12 cm.

Answer

The perimeter of the triangle is 12 cm.