Question

Одна сторона треугольника на 7 см короче другой ее стороны, а диагональ равна 13. Найдите стороны прямоугольника. ПОМОГИТЕ РЕШИТЬ В ВИДЕ СИСТЕМЫ УРАВНЕНИЙ....

Answer 1

Y-большая сторона, x-меньшая сторона. составляем систему: {y-x=7, x^2+y^2=13^2; y=x+7. подставляем во 2 уравнение: x^2+(x+7)^2-169=0; x^2+x^2+14x+49-169=0; 2x^2+14x-120=0; x^2+7x-60=0; D=7^2-4*1*(-60)=49+240=289; x1=(-7-17)/2, x2= (-7+17)/2. x1= -12(не подходит по смыслу задачи), x2=5(см). y=5+7=12(см). Ответ: большая сторона равна 12 см, меньшая сторона равна 5 см.

Answer 2

Problem Analysis

We are given a triangle where one side is 7 cm shorter than the other side, and the diagonal of the triangle is 13 cm. We need to find the sides of the rectangle.

Solution

Let's assume the longer side of the triangle is x cm. Then the shorter side will be (x - 7) cm. We can use the Pythagorean theorem to find the length of the diagonal.

According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's set up the equation using the given information:

(x - 7)^2 + x^2 = 13^2

Simplifying the equation:

x^2 - 14x + 49 + x^2 = 169

2x^2 - 14x - 120 = 0

Now we have a quadratic equation. We can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -14, and c = -120.

Substituting the values into the formula:

x = (-(-14) ± √((-14)^2 - 4 * 2 * -120)) / (2 * 2)

Simplifying further:

x = (14 ± √(196 + 960)) / 4

x = (14 ± √1156) / 4

x = (14 ± 34) / 4

Now we have two possible values for x:

x1 = (14 + 34) / 4 = 48 / 4 = 12

x2 = (14 - 34) / 4 = -20 / 4 = -5

Since the length of a side cannot be negative, we discard the negative value.

Therefore, the longer side of the triangle is 12 cm, and the shorter side is (12 - 7) = 5 cm.

To find the sides of the rectangle, we can use the formula for the perimeter of a rectangle:

Perimeter = 2 * (length + width)

In this case, the length is 12 cm and the width is 5 cm.

Plugging in the values:

Perimeter = 2 * (12 + 5) = 2 * 17 = 34 cm

So, the perimeter of the rectangle is 34 cm.

Answer

The longer side of the triangle is 12 cm, the shorter side is 5 cm, and the perimeter of the rectangle is 34 cm.