Question

Середня лінія трапеції дорівнює 14 см. Знайдіть основи трапеції, якщо одна з них на 4 см менша від другої.​

Answer 1

Ответ:

Средняя линия 1/2(a+b), b=a+4

$\frac{a + a + 4}{2} = 14 \\ 2a + 4 = 28 \\ 2a = 24 \\ a = 12$

$b = 12 + 4 = 16$

Меньшее основания 12 см, а большее 16

Answer 2

Finding the Bases of a Trapezoid

To find the bases of a trapezoid, we need to use the given information that the length of the median is 14 cm and one of the bases is 4 cm shorter than the other.

Let's denote the lengths of the bases as x and y, where x is the shorter base and y is the longer base.

According to the given information, we have the following equation:

x + y = 14 (equation 1)

We also know that one of the bases is 4 cm shorter than the other. This can be expressed as:

x = y - 4 (equation 2)

To find the values of x and y, we can solve these two equations simultaneously.

Substituting equation 2 into equation 1, we get:

(y - 4) + y = 14

Simplifying the equation, we have:

2y - 4 = 14

Adding 4 to both sides of the equation, we get:

2y = 18

Dividing both sides of the equation by 2, we find:

y = 9

Substituting the value of y back into equation 2, we can solve for x:

x = 9 - 4

Simplifying the equation, we have:

x = 5

Therefore, the shorter base (x) of the trapezoid is 5 cm, and the longer base (y) is 9 cm.