#### Answer

x=6; l =15; w=8

#### Work Step by Step

The formula to find the perimeter of a rectangle is P=w+l+w+l, or P=2(l+w). In this case, the width= 2x+3, the length is x+2, and the perimeter is 46. When we input this in the formula, we get 46=2(2x+3+x+2) which can be simplified to 46=2(3x+5) then to 46=6x+10. The goal is to isolate "x", so we need to subtract 10 over to get 36=6x. The final step is to divide 6 on both sides which results in x=6.
The next thing this problem asks is to find the length of each side. We can do this by inputting the value of x into the known length (longer side) value: 2x+3, which makes it 2(6)+3. Simplify that and the value of the length comes out to be 15!
For the other side, you would put 6 in x+2, making it 6+2. The length of the width is 8!
You can check your work by adding all the sides together again.
46=2(8+15)
46=2(23)
46=46