Final answer:
To solve for the lengths of sides RS and ST in parallelogram RSTU, the perimeter formula is rearranged with the given information to find ST = 12 cm and RS = 9 cm. The correct option is C. RS = 9 cm, ST = 12 cm.
Step-by-step explanation:
To find the lengths of sides RS and ST of parallelogram RSTU, we need to use the given information about the perimeter and the relationship between the sides. We're told that side RS is 3 centimeters shorter than side ST and that the perimeter of the parallelogram is 42 centimeters.
Let's denote the length of side ST as x. Since RS is 3 centimeters shorter, its length will be x - 3. In a parallelogram, opposite sides are equal in length, which means we have two sides of length x and two sides of length x - 3.
The formula for the perimeter (P) of a parallelogram is:
P = 2x + 2(x - 3)
Substituting the total perimeter value:
42 = 2x + 2(x - 3)
42 = 2x + 2x - 6
42 = 4x - 6
Adding 6 to both sides of the equation, we get:
48 = 4x
Dividing both sides by 4 gives us:
x = 12
So, ST = 12 cm, and RS (which is 3 cm shorter) = 9 cm.
The correct answer is:
C. RS = 9 cm, ST = 12 cm