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So, we must find the side PQ of the given rectangle PQRS. We are given the side SP to be 4x-1 and side SR to be 3x+3. Since two sides are the same in a rectangle, SP = RQ and PQ = SR. We use the perimeter formula to find the dimensions of PQ such that
2l + 2w = P
2(4x-1) + 2(3x+3) = 116.........Then we solve for x such that we distribute first
8x - 2 + 6x + 6 = 116.........Then add like terms
14x + 4 = 116..........Subtract 4
14x = 112...............Divide 14
x = 8 units
Then, since Side PQ = SR we get PQ = 3x+3 = 3(8)+3 = 27 units.
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