Question

Вычисли площадь прямоугольника, периметр которого равен 24 см, а ширина короче длины в 2 раза

Answer 1

Р = (а + в) * 2 - формула периметра прямоугольника
Р = 24 см - периметр; а = х (см) - ширина; b = 2х (см) - длина
Уравнение: х + 2х = 24 : 2
                    3х = 12
                    х = 4 (см) - ширина (a)
                    2 * 4 = 8 (см) - длина (b)
S = a * b - формула площади прямоугольника
S = 4 * 8 = 32 (кв.см) - площадь прямоугольника
Ответ: 32 кв.см.

Answer 2

Calculating the Area and Perimeter of a Rectangle

To calculate the area and perimeter of a rectangle, we can use the following formulas:

1. Perimeter of a Rectangle (P): - The perimeter of a rectangle is given by the formula: \( P = 2 \times (a + b) \), where \( a \) and \( b \) are the length and width of the rectangle, respectively.

2. Area of a Rectangle (S): - The area of a rectangle is given by the formula: \( S = a \times b \), where \( a \) and \( b \) are the length and width of the rectangle, respectively.

Given that the perimeter of the rectangle is 24 cm and the width is shorter than the length by a factor of 2, we can proceed with the calculations.

Calculations

Let's denote the length of the rectangle as \( l \) and the width as \( w \). We are given that the perimeter is 24 cm and the width is shorter than the length by a factor of 2.

We can set up the following equations: 1. \( 2 \times (l + w) = 24 \) 2. \( w = \frac{l}{2} \)

Solving for Length and Width

We can solve the first equation for \( l \) in terms of \( w \): \[ l = 12 - w \]

Substituting this into the second equation: \[ w = \frac{12 - w}{2} \] \[ 2w = 12 - w \] \[ 3w = 12 \] \[ w = 4 \]

So, the width of the rectangle is 4 cm. Substituting this back into the first equation: \[ 2 \times (l + 4) = 24 \] \[ l + 4 = 12 \] \[ l = 8 \]

So, the length of the rectangle is 8 cm.

Calculating Area and Perimeter

Now that we have the length and width, we can calculate the area and perimeter of the rectangle.

1. Area (S): - \( S = 8 \times 4 = 32 \, \text{cm}^2 \)

2. Perimeter (P): - \( P = 2 \times (8 + 4) = 24 \, \text{cm} \)

Therefore, the area of the rectangle is 32 square centimeters, and the perimeter is 24 centimeters.