Question

середня лінія трапеції дорівнює 10 см. знайдіть основи трапеції, якщо одна з них на 2 см більша за другу

Answer 1

Ответ:

за властивістю середньої лінії трапеції

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 10 cm and one base is 2 cm longer than the other.

Let's assume that the shorter base of the trapezoid is x cm. Since the longer base is 2 cm longer than the shorter base, the length of the longer base can be expressed as (x + 2) cm.

The median of a trapezoid is the line segment that connects the midpoints of the two bases. In this case, the median has a length of 10 cm.

To find the bases, we can use the formula for the length of the median of a trapezoid:

Median = (Sum of the lengths of the bases) / 2

Substituting the given values into the formula, we have:

10 = (x + (x + 2)) / 2

Simplifying the equation, we get:

20 = 2x + 2

Subtracting 2 from both sides, we have:

18 = 2x

Dividing both sides by 2, we get:

x = 9

Therefore, the shorter base of the trapezoid is 9 cm, and the longer base is 9 + 2 = 11 cm.

So, the bases of the trapezoid are 9 cm and 11 cm, respectively.

Please let me know if you need any further assistance!