Question

Знайдіть висоту і середню лінію рівнобічноі трапеціі якщо іі основи дорівнюють 10см і 26см а бічна сторона становить 17см

Answer 1

ср. линия = 1/2*(a+b) = 1/2* (10+26) = 1/2*36 = 18 см

высоты делят трап на прямоугольник и 2 равных прям. тр-ка с гипотенузой 17 и катетом (26-10)/2 = 8 см , второй катет равен h

по т. пифагора: h=√289-64=√225=15 см

 

высота равна 15 см, средняя линия 18 см

Answer 2

Finding the Height and Median Line of an Isosceles Trapezoid

To find the height and median line of an isosceles trapezoid, we need to know the lengths of its bases and one of its lateral sides. In this case, the lengths of the bases are given as 10 cm and 26 cm, and the length of the lateral side is given as 17 cm.

Let's start by finding the height of the trapezoid. The height is the perpendicular distance between the bases. To find it, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In our case, we can consider the height as the hypotenuse, with the bases as the other two sides of the right triangle. Let's call the height 'h', the shorter base 'a' (10 cm), and the longer base 'b' (26 cm).

Using the Pythagorean theorem, we can write the equation:

h^2 = b^2 - a^2

Substituting the given values, we have:

h^2 = 26^2 - 10^2

Simplifying the equation:

h^2 = 676 - 100

h^2 = 576

Taking the square root of both sides, we find:

h = 24 cm

So, the height of the trapezoid is 24 cm.

Next, let's find the median line of the trapezoid. The median line is the line segment connecting the midpoints of the non-parallel sides of the trapezoid. In an isosceles trapezoid, the median line is parallel to the bases and its length is equal to the average of the lengths of the bases.

In this case, the lengths of the bases are 10 cm and 26 cm. The average of these lengths is:

average = (10 + 26) / 2 = 36 / 2 = 18 cm

Therefore, the length of the median line is 18 cm.

To summarize: - The height of the trapezoid is 24 cm. - The length of the median line is 18 cm.

Please let me know if there's anything else I can help you with!