Question

периметр прямоугольника равен 76 см. найди его площадь если ширина меньше длинны на 4 см

Answer 1

х+(х+4)*2=76

2х=76/2-4

2х=34

х=17  

 

17-ширина прямоугольника , следовательно 17+4=21 - длина прямоугольника , найдем площадь

S=a*b=17*21=357 

 

Ответ : 357

Answer 2

Пусть ширина будет х, тогда длина будет (х+4), составим уравнение:

Периметр - это сумма всех сторон.

2·х+2·(х+4)=76

2х+2х+8=76

4х=76-8

4х=68

х=68:4

х=17

Значит ширина составляет 17 см, а длина (х+4)=17+4=21 см

Найдем площадь:

17·21=357 см²

Answer 3

Calculating the Area of a Rectangle

To find the area of a rectangle when the perimeter is given and the width is 4 cm less than the length, we can use the following steps:

1. Identify the Perimeter and Relationship Between Length and Width: - The perimeter of a rectangle is given by the formula: \( P = 2 \times (length + width) \). - We are given that the perimeter \( P \) is 76 cm and the width \( w \) is 4 cm less than the length \( l \).

2. Calculate the Length and Width: - We can set up an equation using the given information to find the length and width of the rectangle.

3. Use the Length and Width to Calculate the Area: - Once we have the length and width, we can use the formula for the area of a rectangle: \( A = length \times width \).

Solution

1. Identify the Perimeter and Relationship Between Length and Width: - The perimeter \( P \) of a rectangle is given by the formula: \( P = 2 \times (length + width) \).

2. Calculate the Length and Width: - Let's denote the length as \( l \) and the width as \( w \). - We are given that the perimeter \( P \) is 76 cm and the width \( w \) is 4 cm less than the length \( l \). - Using the given information, we can set up the following equation: - \( P = 2 \times (l + w) \) - \( w = l - 4 \)

- Substituting the expression for \( w \) into the perimeter formula: - \( 76 = 2 \times (l + (l - 4)) \) - \( 76 = 2 \times (2l - 4) \) - \( 38 = 2l - 4 \) - \( 2l = 42 \) - \( l = 21 \)

- Using the value of \( l \) to find \( w \): - \( w = 21 - 4 \) - \( w = 17 \)

3. Use the Length and Width to Calculate the Area: - Now that we have the length \( l = 21 \) cm and the width \( w = 17 \) cm, we can calculate the area \( A \) using the formula: \( A = length \times width \). - \( A = 21 \times 17 \) - \( A = 357 \, cm^2 \)

Answer

The area of the rectangle is 357 square centimeters.