Question

В параллелограмме ABCD диагональ BD перпендикулярна стороне AD.Найдите AC, если AD = 6 см, BD = 5 см.Было бы отлично,если был бы рисунок.Заранее спасибо!

Answer 1

Пусть О - точка пересечения диагоналей.
Как известно в параллелограмме диагонали в точке пересечения делятся пополам.
Из прямоугольного треугольника АОD:
AO^2=AD^2+DO^2 = AD^2+(BD/2)^2 = 6^2+(5/2)^2 = 36+6,25 = 42,25.
AO=√42,25 = 6,5.
AC=2*AO= 2*6,5 = 13 (см).

Answer 2

Finding the length of AC in a parallelogram

To find the length of AC in a parallelogram ABCD, where diagonal BD is perpendicular to side AD, we can use the fact that in a parallelogram, the sum of the squares of the lengths of the diagonals is equal to the sum of the squares of the lengths of the sides.

Let's denote the length of AC as x.

According to the given information: - AD = 6 cm - BD = 5 cm

Using the formula for the sum of the squares of the lengths of the diagonals in a parallelogram, we have:

AC^2 + BD^2 = AD^2 + BC^2

Substituting the given values, we get:

x^2 + 5^2 = 6^2 + BC^2

Simplifying the equation:

x^2 + 25 = 36 + BC^2

x^2 = 36 + BC^2 - 25

x^2 = 11 + BC^2

To find the value of BC, we can use the fact that in a parallelogram, opposite sides are equal in length. Since AD and BC are opposite sides, we have:

BC = AD = 6 cm

Substituting this value into the equation:

x^2 = 11 + 6^2

x^2 = 11 + 36

x^2 = 47

Taking the square root of both sides:

x = √47

Therefore, the length of AC is approximately 6.855 cm.

Please note that the above calculations are based on the given information and assumptions about the properties of a parallelogram. If there are any additional constraints or information, please let me know, and I'll be happy to assist you further.