Hello there. To solve this question, we'll have to remember some properties about finding the perimeter of a rectangle.
First, knowing that parallel sides on a rectangle have equal measures, we know that:
RQ also measures 3y + 3 and PQ measures 2y.
Now, the perimeter is adding the measures of all the sides of the rectangle. We have that:
PS + SR + RQ + PQ = 3y + 3 + 2y + 3y + 3 + 2y = 10y + 6
Knowing that this perimeter is equal to 96, we make:
96 = 10y + 6
Subtract 6 on both sides of the equation
10y = 90
Divide both sides of the equation by a factor of 10
y = 9
Now, to find the measure of the side PS, we plug in the value we found for y in the expression for the side
3 * 9 + 3
Multiply and add the values
27 + 3
30
