Question

периметр четырёхугольнику равен 32 см.Диагональ делит его на 2 треугольника с периметрами 28 и 16 см.Найти длину диоганали.(если можно с решением).

Answer 1

ABCD-четырехугольник
P (ABCD)-AB+BC+CD+AD=32
P (ABC)-AB+BC+AC=28
P (ACD)-AC+CD+AC=16
AB+BC+AC=28 (1)
AC+CD+AD=16 (2)
Ур-ние (1)+(2)=>
AB+BC+AC+AC+CD+AD=28+16
(AB+BC+CD+AD)+2AC=44
AB+BC+CD+AD=32
32+2AC=44
AC=(44-32):2=6 - Диагональ
 

Answer 2

P четырехугольника=32, P 1треуг=16,Р2треуг.=28=>Р1+Р2=28+16=44

Р четырехугольника=(Р1+Р2)-Р =44-32=12

Ответ:12

Answer 3

Problem Analysis

We are given a quadrilateral with a perimeter of 32 cm. The diagonal divides the quadrilateral into two triangles with perimeters of 28 cm and 16 cm. We need to find the length of the diagonal.

Solution

Let's assume the lengths of the sides of the quadrilateral are a, b, c, and d. The perimeter of the quadrilateral is the sum of the lengths of its sides: P = a + b + c + d.

We are also given that the diagonal divides the quadrilateral into two triangles with perimeters of 28 cm and 16 cm. Let's assume the lengths of the sides of the triangles are x, y, and z. Therefore, we have the following equations:

Equation 1: a + b + x = 28 Equation 2: c + d + x = 16

To find the length of the diagonal, we need to find the value of x.

Let's solve the equations to find the values of a, b, c, d, and x.

From Equation 1, we can express x in terms of a and b: x = 28 - (a + b)

From Equation 2, we can express x in terms of c and d: x = 16 - (c + d)

Setting the two expressions for x equal to each other, we have: 28 - (a + b) = 16 - (c + d)

Rearranging the equation, we get: (a + b) - (c + d) = 28 - 16 a + b - c - d = 12

Since the perimeter of the quadrilateral is 32 cm, we have: a + b + c + d = 32

Adding the two equations, we get: 2(a + b) = 44 a + b = 22

Substituting this value back into the equation a + b - c - d = 12, we have: 22 - c - d = 12 c + d = 22 - 12 c + d = 10

Now we have the following system of equations: a + b = 22 c + d = 10

To find the length of the diagonal, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the sides a, b, c, and d.

Using the Pythagorean theorem, we have: diagonal^2 = (a + c)^2 + (b + d)^2

Substituting the values we found, we have: diagonal^2 = (22)^2 + (10)^2 diagonal^2 = 484 + 100 diagonal^2 = 584

Taking the square root of both sides, we get: diagonal = √584 diagonal ≈ 24.17 cm

Therefore, the length of the diagonal is approximately 24.17 cm.

Answer

The length of the diagonal is approximately 24.17 cm.