Length of diagnols AC andBD of a rhombus are 6cm and 8cm respectively. Find the length of each side of rhombus
a^2 + b^2 = c^2 (pythagorus theorem)
Since diagonals of rhombus bisect perpendicular
Then 3^ + 4^2 = c^2 but c = L
L = 5 cm
To find the length of each side of a rhombus, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a rhombus, the diagonals are actually the perpendicular bisectors of each other, which means that they divide the rhombus into four congruent right triangles.
Let's denote the length of each side of the rhombus as "s".
Using the given information, we can consider one of the right triangles formed by the diagonals. In this triangle, the diagonal AC is the hypotenuse, with a length of 6 cm, and the side lengths are s/2 and s/2 (since the diagonals bisect each other).
Applying the Pythagorean theorem, we have:
(s/2)^2 + (s/2)^2 = AC^2
(s^2/4) + (s^2/4) = 6^2
s^2/2 = 36
s^2 = 72
s = √72
Thus, the length of each side of the rhombus is √72 cm.