Question

1 решите задачю споможью уравнения.длина примоугольника на 8см больше его ширены.найдите стороны прямоугольника если его площадь равна 65 см. вопрос жизни и смерти пожалуйста решите да 50 балов пж по брадски ​

Answer 1

Ответ:

Объяснение:

ширина - х см, длина (х+8) см, х*(х+8)=65 - площадь, решаем уравнение:

х²+8х-65=0

D=324, √D=+-18;

х₁= -13 (не подходит)

х₂= 5 см - ширина, (5+8)=13 см - длина.

Answer 2

Problem Analysis

We are given that the length of a rectangle is 8 cm longer than its width, and the area of the rectangle is 65 cm². We need to find the dimensions of the rectangle.

Solution

Let's assume the width of the rectangle is x cm. According to the problem, the length of the rectangle is 8 cm longer than its width, so the length would be x + 8 cm.

The area of a rectangle is given by the formula: Area = Length × Width.

Substituting the given values, we have: 65 = (x + 8) × x

To solve this equation, we can expand it and rearrange it to form a quadratic equation: x² + 8x - 65 = 0

Now, we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

We can solve the quadratic equation using various methods, such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the value of x.

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

For our equation x² + 8x - 65 = 0, the coefficients are: a = 1, b = 8, and c = -65.

Substituting these values into the quadratic formula, we get: x = (-8 ± √(8² - 4(1)(-65))) / (2(1))

Simplifying further: x = (-8 ± √(64 + 260)) / 2 x = (-8 ± √324) / 2 x = (-8 ± 18) / 2

Now, we have two possible values for x: 1. x = (-8 + 18) / 2 = 10 / 2 = 5 2. x = (-8 - 18) / 2 = -26 / 2 = -13

Since the width of a rectangle cannot be negative, we discard the second solution x = -13.

Therefore, the width of the rectangle is 5 cm.

To find the length, we can substitute this value back into the equation Length = Width + 8: Length = 5 + 8 = 13 cm

So, the dimensions of the rectangle are: Width = 5 cm and Length = 13 cm.

Answer

The dimensions of the rectangle are 5 cm (width) and 13 cm (length).