Question

Даны прямоугольник и квадрат. Длина прямоугольника 12 см. Сторона квадрата на 1 см меньше, чем ширина прямоугольника. Периметр квадрата на 10 см меньше, чем периметр прямоугольника. Найдите ширину прямоугольника

Answer 1

Пусть х см- это ширина прямоугольника, тогда сторона квадрата (х-1) смПериметр прямоугольника = 2(12+x)-10, а периметр квадрата 4(x-1), соблюдая условие получаем:2(12+х)-10=4(x-1)24+2x-10=4x-42x-4x=10-4-24-2x=-18x=9 (см) - ширина прямоугольника

Answer 2

Understanding the problem

Let's break down the given information to understand the problem:

- Length of the rectangle = 12 cm - Side of the square = 1 cm less than the width of the rectangle - Perimeter of the square = 10 cm less than the perimeter of the rectangle

We need to find the width of the rectangle.

Solution

Let's denote the width of the rectangle as "w" and the side of the square as "s".

We know that the length of the rectangle is 12 cm. So, the dimensions of the rectangle are 12 cm x w.

The side of the square is 1 cm less than the width of the rectangle. So, we can write the equation:

s = w - 1

The perimeter of the rectangle is given by the formula:

Perimeter of rectangle = 2 * (Length + Width)

And the perimeter of the square is given by the formula:

Perimeter of square = 4 * Side

According to the problem, the perimeter of the square is 10 cm less than the perimeter of the rectangle. So, we can write the equation:

Perimeter of rectangle - Perimeter of square = 10

Substituting the formulas for the perimeters and the values we know, we get:

2 * (12 + w) - 4s = 10

Now, we can substitute the value of "s" from the first equation into the second equation:

2 * (12 + w) - 4(w - 1) = 10

Simplifying the equation:

24 + 2w - 4w + 4 = 10

Combine like terms:

28 - 2w = 10

Rearrange the equation:

-2w = 10 - 28

-2w = -18

Divide both sides by -2:

w = -18 / -2

w = 9

Therefore, the width of the rectangle is 9 cm.

Please note that negative values for width or any physical dimension are not meaningful. So we can consider the width of the rectangle as 9 cm.