Найди длину высоты треугольника OAB, опущенную на сторону АВ, если периметр треугольника ОНВ составляет 24 см, а диматер изображенной окружности равен 20 см, АВ = 12 см.

The height of triangle OAB is 8 cm

Step-by-step explanation:

The question in English is

Find the length of the height of the triangle OAB dropped to the side of AB, if the perimeter of the triangle OHV is 24 cm, and the diameter of the circle shown is 20 cm, AB = 12 cm.

The picture of the question in the attached figure

we know that

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc

In this problem the diameter of the circle CD is perpendicular to the chord AB, that means that the diameter bisect the chord

so

Remember that the perimeter of triangle is equal to the sum of its three length sides

so

Perimeter of triangle OHB is given by

we have

---> the radius is half the diameter

substitute the given values

solve for OH

therefore

The height of triangle OAB is 8 cm

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

x = 3 ± √(5+y)