Answer: 18.5 cm
Step-by-step explanation:
The diagonals of a rhombus are perpendicular bisectors so we can use the Pythagorean Theorem to find the side length of the rhombus. Remember that the sides of a rhombus are congruent (equal) so if we find the length of one side, we have found the lengths of all of the sides.
[tex]\bigg(\dfrac{35}{2}\bigg)^2+\bigg(\dfrac{12}{2}\bigg)^2=c^2\\\\\\17.5^2+6^2=c^2\\\\306.25+36=c^2\\\\342.25\quad =c^2\\\\\sqrt{342.25}=c\\\\\large\boxed{18.5}=c[/tex]
So, each side of the rhombus is 18.5 cm.
