Answer: The length of the other diagonal is approximately 5.83 cm (rounded to two decimal places).
Explanation:
Label the diagonals of the rhombus as d1 and d2. Since the diagonals of a rhombus intersect at a 90-degree angle, we can use the Pythagorean theorem to relate the diagonals and the side length:
d1^2 = (6/2)^2 + (d2/2)^2
d1^2 = 9 + (d2/2)^2
We also know that the length of one diagonal is 10cm:
d2 = 10
We can substitute this value into the equation for d1:
d1^2 = 9 + (10/2)^2
d1^2 = 9 + 25
d1^2 = 34
Taking the square root of both sides, we get:
d1 = sqrt(34)