Question

Пожалуста Діагоналі паралелограма 14 і 22 см а сторони пропорційні числам 6 і 7. Знайдіть периметр паралелограма

Answer 1

Дано
АВСД - паралелограм; АВ\\СД, ВС\\АД.
АС=22 см, ВД=14 см; АВ\АД=6\7
Знайти Р.

Нехай АВ=6х см, а ВС=7х см.
За властивістю діагоналей паралелограма
АС²+ВД²=2(АВ²+ВС²)
484+196=2[(6x)²+(7x)²]
680=2(36х²+49х²)
170х²=680
х²=4
х=2.
АВ=6*2=12 см; АД=7*2=14 см.
Р=2(12+14)=2*26=52 см.
Відповідь: 52 см.

Answer 2

Finding the Perimeter of a Parallelogram

To find the perimeter of a parallelogram, we need to know the lengths of its sides. In this case, we are given that the diagonals of the parallelogram are 14 cm and 22 cm, and the sides are proportional to the numbers 6 and 7.

Let's assume that the length of one side of the parallelogram is 6x, where x is a constant. Since the sides are proportional to the numbers 6 and 7, the length of the other side would be 7x.

Now, let's use the given information about the diagonals. In a parallelogram, the diagonals bisect each other, meaning they divide each other into two equal parts. Therefore, we can say that half of the diagonal length is equal to the sum of the sides.

For the first diagonal of 14 cm, we have:

14/2 = 6x + 7x

Simplifying the equation:

7 = 13x

Solving for x:

x = 7/13

Now, we can find the lengths of the sides:

Side AB = 6x = 6 * (7/13) = 42/13 cm

Side BC = 7x = 7 * (7/13) = 49/13 cm

To find the perimeter of the parallelogram, we add up the lengths of all four sides:

Perimeter = 2 * (AB + BC)

Substituting the values we found:

Perimeter = 2 * (42/13 + 49/13) = 2 * (91/13) = 182/13 cm

Therefore, the perimeter of the parallelogram is 182/13 cm.