Finding the length of a rectangle given the perimeter and 2 sides

Question

The perimeter of the rectangle below is 116 units. Find the length of side PQ. Side SP= 4x-1 and Side SR= 3x+3. Write you answers without variables. 

Answer 1

Greetings! Lets solve this shall we ?

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.

I hope this helped!