Question

Периметр прямокутника 46 см . діагональ дорівнює 17 см . знайти сторони прямокутника

Answer 1

Периметр прямоугольника равен сумме всех его сторон, у него по две одинаковые стороны. Поэтому  его периметр= 2a+2b=46 . Составим систему неравенств a+b=23 отсюда a=23-b, находим по теореме пифагора стороны: (23-b)в квадрате+ и в квадрате =17 отсюда b=8,а сторона а,в свою очередь будет равна 15 так как 64+а в квадрате=289. Ответ: стороны прямоугольника равны 15 и 8

Answer 2

Finding the Sides of a Rectangle Given the Perimeter and Diagonal

To find the sides of a rectangle when the perimeter and diagonal are given, we can use the following steps:

1. Let's assume the length of the rectangle is a and the width is b. 2. The perimeter of a rectangle is given by the formula: Perimeter = 2(a + b). 3. We are given that the perimeter is 46 cm, so we can write the equation: 46 = 2(a + b).

Now, let's find the value of b in terms of a using the given diagonal.

4. The diagonal of a rectangle can be found using the Pythagorean theorem: Diagonal = sqrt(a^2 + b^2). 5. We are given that the diagonal is 17 cm, so we can write the equation: 17 = sqrt(a^2 + b^2).

By solving these two equations simultaneously, we can find the values of a and b.

Let's solve the equations:

From equation 1: 46 = 2(a + b), we can simplify it to: 23 = a + b. (Equation 1)

From equation 2: 17 = sqrt(a^2 + b^2), we can square both sides to eliminate the square root: 289 = a^2 + b^2. (Equation 2)

Now, we can solve these equations simultaneously.

Substitute equation 1 into equation 2:

289 = a^2 + (23 - a)^2

Simplifying the equation:

289 = a^2 + 529 - 46a + a^2

Combining like terms:

2a^2 - 46a + 240 = 0

Now, we can solve this quadratic equation to find the values of a and b.

Using the quadratic formula: a = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = 2, b = -46, and c = 240.

Calculating the discriminant: b^2 - 4ac = (-46)^2 - 4(2)(240) = 2116 - 1920 = 196.

Since the discriminant is positive, we have two real solutions.

Using the quadratic formula:

a = (-(-46) ± sqrt(196)) / (2(2))

Simplifying:

a = (46 ± 14) / 4

This gives us two possible values for a:

1. When a = (46 + 14) / 4 = 60 / 4 = 15 2. When a = (46 - 14) / 4 = 32 / 4 = 8

Now, we can substitute these values of a into equation 1 to find the corresponding values of b.

For a = 15: 23 = 15 + b b = 23 - 15 = 8

For a = 8: 23 = 8 + b b = 23 - 8 = 15

Therefore, the sides of the rectangle can be either 15 cm x 8 cm or 8 cm x 15 cm.

Please note that the given search results did not provide a direct answer to the question. The solution provided above is based on the standard method of finding the sides of a rectangle given the perimeter and diagonal.