Final answer:
The perimeter of rhombus JOSE is 52 cm, calculated by solving the equation 3x - 5 = 13 to find the length of one side and then multiplying that length by 4.
Step-by-step explanation:
To find the perimeter of rhombus JOSE, we need to recognize that all sides of a rhombus are of equal length. Given that JO = 3x - 5 and an actual measurement of side OS is 13 cm, we can set 3x - 5 equal to 13 cm to solve for x:
3x - 5 = 13
3x = 13 + 5
3x = 18
x = 6
Now that we know x = 6, we can find the actual length of each side:
JO = 3(6) - 5
JO = 18 - 5
JO = 13 cm
Since all sides of a rhombus are equal, to find the perimeter (P), we multiply the length of one side by 4, because a rhombus has 4 sides:
P = 4 × side length
P = 4 × 13 cm
P = 52 cm
Therefore, the perimeter of rhombus JOSE is 52 cm.