Question

СРОЧНО!!!!!!!!!!!!Центр кола, вписаного в прямокутну трапецію, віддалений від кінців її бічної сторони відповідно на 15см і 20см. Обчисліть периметр цієї трапеції. Дуже треба​

Answer 1

Відповідь:

145 см.

Пояснення:

Дано:

r1 = 15 см

r2 = 20 см

a = 20 см.

b = 15 см.

Знайти:

$P_{T}$

Формула для обчислення периметра трапеції:

P = a + b + 2r + 2r

Підставимо відомі значення в формулу:

P = 20 см + 15 см + 2(15 см) + 2(20 см)

Розрахунок:

P = 35 см + 30 см + 40 см + 40 см = 145 см

Answer 2

To calculate the perimeter of the trapezium, we need to know the lengths of all its sides. In this case, we are given that the center of the circle inscribed in the trapezium is located 15 cm away from one of its lateral sides and 20 cm away from the other lateral side.

To find the perimeter, we can use the formula:

Perimeter = sum of all sides

Let's denote the lengths of the sides as follows: - The length of the shorter parallel side of the trapezium as a - The length of the longer parallel side of the trapezium as b - The length of one of the lateral sides of the trapezium as c - The length of the other lateral side of the trapezium as d

According to the given information, we have: - The distance from the center of the inscribed circle to one of the lateral sides is 15 cm, which is equal to half the length of the shorter parallel side: c = a/2 - The distance from the center of the inscribed circle to the other lateral side is 20 cm, which is equal to half the length of the longer parallel side: d = b/2

To find the perimeter, we need to express the lengths of all sides in terms of a and b.

Length of the shorter parallel side (a):

Since the distance from the center of the inscribed circle to one of the lateral sides is 15 cm, we can express a in terms of c as follows: a = 2c = 2(a/2) = a

Length of the longer parallel side (b):

Similarly, since the distance from the center of the inscribed circle to the other lateral side is 20 cm, we can express b in terms of d as follows: b = 2d = 2(b/2) = b

Now, we can express the perimeter of the trapezium in terms of a and b:

Perimeter = a + b + c + d

Substituting the expressions for a and b that we derived earlier, we get:

Perimeter = a + b + (a/2) + (b/2)

Simplifying the expression, we have:

Perimeter = (3a + 3b)/2

Therefore, the perimeter of the trapezium is given by (3a + 3b)/2.

Please provide the values of a and b so that we can calculate the perimeter for you.