Question

Срочно, Площа прямокутника дорівнює 154 см2, а його периметр - 50 см. Знайди сторони прямокутника​

Answer 1

Ответ:

Объяснение:

на фото

Answer 2

Calculation of Rectangle Sides

To find the sides of a rectangle when given its area and perimeter, we can use the following formulas:

1. Let's assume the length of the rectangle is L and the width is W. 2. The area of a rectangle is given by the formula: Area = Length × Width. 3. The perimeter of a rectangle is given by the formula: Perimeter = 2 × (Length + Width).

Given that the area of the rectangle is 154 cm² and the perimeter is 50 cm, we can set up the following equations:

1. Area = Length × Width => 154 = L × W (Equation 1) 2. Perimeter = 2 × (Length + Width) => 50 = 2 × (L + W) (Equation 2)

To solve these equations, we can use substitution or elimination methods. Let's use the substitution method:

From Equation 1, we can express L in terms of W: L = 154 / W (Equation 3)

Substituting Equation 3 into Equation 2, we get: 50 = 2 × (154 / W + W)

Simplifying the equation further: 25 = 154 / W + W

To solve this equation, we can multiply both sides by W to eliminate the fraction: 25W = 154 + W²

Rearranging the equation: W² + 25W - 154 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by: W = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 1, b = 25, and c = -154. Substituting these values into the quadratic formula, we get:

W = (-25 ± √(25² - 4 × 1 × -154)) / (2 × 1)

Simplifying further: W = (-25 ± √(625 + 616)) / 2 W = (-25 ± √1241) / 2

Calculating the square root of 1241, we get: W ≈ (-25 ± 35.22) / 2

Now we have two possible values for W: 1. W ≈ (-25 + 35.22) / 2 ≈ 5.11 2. W ≈ (-25 - 35.22) / 2 ≈ -30.22

Since the width of a rectangle cannot be negative, we discard the second solution.

Now that we have the value of W, we can substitute it back into Equation 3 to find the value of L: L = 154 / W ≈ 154 / 5.11 ≈ 30.15

Therefore, the sides of the rectangle are approximately: Length (L) ≈ 30.15 cm Width (W) ≈ 5.11 cm

Please note that these values are approximate due to rounding.