Question

Основи трапеції відносяться як 4: 5, а середня лінія дорівнює 9 см. Знайдіть основи.​

Answer 1

Основания трапеции равны 8 и 10 см

Answer 2

Finding the Bases of a Trapezoid

To find the bases of a trapezoid, we need to use the given information. According to the question, the ratio of the bases is 4:5, and the length of the median line is 9 cm.

Let's assume the lengths of the bases are 4x and 5x (where x is a constant).

The formula for the median of a trapezoid is given by:

Median = (Base1 + Base2) / 2

In this case, the median is given as 9 cm. Substituting the values, we get:

9 = (4x + 5x) / 2

To solve for x, we can multiply both sides of the equation by 2:

18 = 4x + 5x

Combining like terms, we have:

18 = 9x

Dividing both sides by 9, we find:

x = 2

Now that we have the value of x, we can find the lengths of the bases:

Base1 = 4x = 4 * 2 = 8 cm

Base2 = 5x = 5 * 2 = 10 cm

Therefore, the lengths of the bases of the trapezoid are 8 cm and 10 cm.