Question

Решите задачу с помощью уравнения.длина прямоугольника на 8 см больше его ширины. Найдите стороны прямоугольника, если его площадь равна 144 см во второй степени. ДАЮ 100 баллов, помогитеее

Answer 1

Ответ:

Сори если не правильно!!

Answer 2

Ответ:

S=ab

a=x

b=x+8

S=x(x+8)

S=x²+8x=144

x²+8x-144=0

D=8²-4×1×(-144) =64+576=640( точно правильно выписал/а? )

х1=-8-√640/2

х2=-8+√640/2

всё таки где-то допустил/а ошибку когда выписывал/а

Answer 3

Problem Analysis

We are given that the length of a rectangle is 8 cm more than its width, and the area of the rectangle is 144 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 more 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: 144 = (x + 8) × x

To solve this equation, we can expand it and rearrange it to form a quadratic equation: x² + 8x - 144 = 0

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

Quadratic Equation Solution

We can solve the quadratic equation using factoring, completing the square, or 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 - 144 = 0, the coefficients are: a = 1, b = 8, and c = -144.

Substituting these values into the quadratic formula, we get: x = (-8 ± √(8² - 4(1)(-144))) / (2(1))

Simplifying further: x = (-8 ± √(64 + 576)) / 2 x = (-8 ± √640) / 2 x = (-8 ± 8√10) / 2 x = -4 ± 4√10

Since the width cannot be negative, we can ignore the negative value. Therefore, the width of the rectangle is: x = -4 + 4√10

To find the length, we can substitute this value back into the equation length = width + 8: length = (-4 + 4√10) + 8 length = 4√10 + 4

Therefore, the dimensions of the rectangle are: Width = -4 + 4√10 cm Length = 4√10 + 4 cm

Answer

The width of the rectangle is -4 + 4√10 cm and the length is 4√10 + 4 cm.