In a rhombus ABCD,diagonals AC and BD are respectively 8cm and 6cm , the length of each side of rhombus is
length of each side of rhombus:
a = sqrt[(AD)^2 + (BD)^2] / 2
Solve.
a = 5 cm
To find the length of each side of the rhombus, we can use the fact that the diagonals of a rhombus bisect each other at a 90-degree angle.
In the given rhombus ABCD, we have:
AC = 8 cm (length of diagonal AC)
BD = 6 cm (length of diagonal BD)
Let's consider the intersection point of the diagonals as point O.
Using the Pythagorean Theorem, we can find the length of OB (half of diagonal BD) and OA (half of diagonal AC).
OA^2 + OB^2 = AB^2 (where AB is the length of each side of the rhombus)
Since the diagonals bisect each other at a 90-degree angle, we can determine that OA and OB form the legs of a right triangle.
Let's substitute the given lengths into the equation:
(8/2)^2 + (6/2)^2 = AB^2
4^2 + 3^2 = AB^2
16 + 9 = AB^2
25 = AB^2
Taking the square root of both sides:
AB = √25
AB = 5 cm
Therefore, the length of each side of the rhombus is 5 cm.