Question

Стороны трапеции относятся как 4:1:6:4, а периметр ее равен 75см. Вычисли стороны трапеции. Длины сторон записывать в таком же порядке, как даны в соотношении.

Answer 1

Calculation of Trapezoid Sides

To calculate the sides of a trapezoid, we can use the given ratio of the sides and the perimeter of the trapezoid.

Let's denote the sides of the trapezoid as follows: - The first side: 4x - The second side: x - The third side: 6x - The fourth side: 4x

According to the given ratio, the sides of the trapezoid are in the ratio 4:1:6:4.

The perimeter of the trapezoid is given as 75 cm.

To find the value of x, we can set up the following equation:

4x + x + 6x + 4x = 75

Simplifying the equation, we get:

15x = 75

Dividing both sides of the equation by 15, we find:

x = 5

Now that we have the value of x, we can calculate the lengths of the sides of the trapezoid:

- The first side: 4x = 4 * 5 = 20 cm - The second side: x = 5 cm - The third side: 6x = 6 * 5 = 30 cm - The fourth side: 4x = 4 * 5 = 20 cm

Therefore, the lengths of the sides of the trapezoid are: - The first side: 20 cm - The second side: 5 cm - The third side: 30 cm - The fourth side: 20 cm

Please note that the lengths of the sides are written in the same order as given in the ratio.