What are the length of each side of a quadrilateral when the perimeter is 33 and the sides are: a a+5 a-3 2a+1

 
A = 6 
So 
Side A = 6 
Side B = 11 
Side C = 3 
Side D = 13

Explanation: 
To solve perimeter of a quadrilateral, you use this formula: 
side A + side B + side C + side D = total perimeter.

If the four sides are A, A + 5, A – 3, and 2A + 1 then you need to solve for A.

Write out an algebraic formula with these values:
A + (A + 5) + (A – 3) + (2A + 1) = P 
You also know that the total perimeter is 33, so :
A + (A + 5) + (A – 3) + (2A + 1) = 33 
You can add all the A values together to combine like terms like this:
5A + 5 – 3 + 1 = 33 
Solve fore A:
5A + 3 = 33 
5A = 33 – 3 
5A = 30 
A = 30 ÷ 5 
A = 6 

Check your  
A + (A + 5) + (A – 3) + (2A + 1) = 33 
(6) + ((6) + 5) + ((6) – 3) + (2(6) + 1) = 33 
(6) + (11) + (3) + (13) = 33 
17 + 16 = 33 
33 = 33