Question

ABCD- ромб , BD=14 , BC = 25 AC=?​

Answer 1

Ответ:
АС=48ед.

Решение:
Диагонали ромба пересекаются перпендикулярно и точкой пересечения делятся пополам.
ВО=ВD/2=14/2=7ед.
Теорема Пифагора
АО=√(АВ²-ВО²)=√(25²-7²)=
=√(625-49)=√576=24ед.
АС=2*АО=2*24=48ед

Answer 2

ABCD is a rhombus, and you're given that BD = 14 and BC = 25. To find the length of AC, we can use the properties of a rhombus.

In a rhombus, the diagonals are perpendicular bisectors of each other, which means they intersect at right angles and divide each other into equal halves. Let's denote the intersection point of the diagonals as O.

Since the diagonals of a rhombus bisect each other, BO = OD = 14/2 = 7. Also, since the diagonals are perpendicular, triangle BOC is a right triangle.

Using the Pythagorean theorem in triangle BOC, we can find the length of BC:

BC^2 = BO^2 + OC^2 25^2 = 7^2 + OC^2 625 = 49 + OC^2 OC^2 = 625 - 49 OC^2 = 576 OC = √576 OC = 24

Now, we know that AC is twice the length of OC because the diagonals of a rhombus divide each other into equal halves. Therefore:

AC = 2 * OC AC = 2 * 24 AC = 48

So, the length of AC is 48 units.