Final answer:
The length of diagonal AC in rhombus ABCD is approximately 6.5 cm.
Step-by-step explanation:
To find the length of diagonal AC in rhombus ABCD, we can use the Pythagorean theorem. In a rhombus, the diagonals intersect at right angles and bisect each other. Let's assume the length of diagonal AC is 'x'. From the given information, we can observe that AE and BE are half the lengths of the diagonals. So, AE = 5cm and BE = 12cm. Using the Pythagorean theorem, we have:
AC^2 = AE^2 + CE^2
x^2 = (5/2)^2 + (12/2)^2
x^2 = 25/4 + 144/4
x^2 = 169/4
Taking the square root of both sides, we get:
x = sqrt(169/4)
x = 13/2
So, the length of diagonal AC is 13/2 cm, which is approximately 6.5 cm.