Question

Стороны прямоугольника относятся как 2 к 6, а его периметр равен 32см найдите площадь этого прямоугольника

Answer 1

Пусть одна сторона прямоугольника 2х см, а  другая 6х см. Тогда 2х:6х=2:6
Периметр прямоугольника-сумма всех его сторон.
2х+6х+2х+6х=32
16х=32
х=2
Одна сторона 2х=2·2=4 см, другая 6х=6·2=12 см
Площадь прямоугольника равна произведению длины на ширину,
S=4·12=48 кв см

Answer 2

Finding the sides of the rectangle

To find the sides of the rectangle, we are given that the ratio of the sides is 2:6. Let's assume the shorter side is 2x and the longer side is 6x.

Calculating the perimeter of the rectangle

The perimeter of a rectangle is given by the formula P = 2(a + b), where a and b are the lengths of the sides. In this case, we have:

P = 2(2x + 6x) = 2(8x) = 16x

We are also given that the perimeter is equal to 32 cm. So we can set up the equation:

16x = 32

Solving for x, we find:

x = 32 / 16 = 2

Finding the area of the rectangle

The area of a rectangle is given by the formula A = length * width. In this case, the length is 6x and the width is 2x. Substituting the value of x, we have:

Length = 6 * 2 = 12 cm Width = 2 * 2 = 4 cm

Therefore, the area of the rectangle is:

A = 12 cm * 4 cm = 48 cm²

So, the area of the rectangle is 48 cm².