Final answer:
The length of side AB of the rhombus ABCD is (2x + 39)/3 cm.
Step-by-step explanation:
Given that the perimeter of the rhombus ABCD is (7x + 39) cm and AD = 5x, we can determine the length of side AB.
A rhombus has equal side lengths, so the perimeter of the rhombus is the sum of all four sides: AB + BC + CD + DA = (7x + 39) cm. Since AD = 5x, we can substitute the value and solve for AB.
AB + BC + CD + (5x) = 7x + 39
AB + BC + CD = 2x + 39
Since a rhombus has opposite sides that are equal in length, we can assume BC and CD are both equal to AB, and we have:
AB + AB + AB = 2x + 39
3AB = 2x + 39
AB = (2x + 39)/3
Therefore, the length of side AB is (2x + 39)/3 cm.