Plug in the area and perimeter amounts into the equation. For example, fill out the two formulas using this information: the area of a rectangle is 24 and the perimeter is 20. The equations read 24 = L x W and 20 = 2(L + W) or 20 = 2L + 2W.
Divide the perimeter equation by 2 to simplify it. When you divide 20 = 2L + 2W, it is reduced to 10 = L + W.
Substitute the area equation into the perimeter equation. To do this, rewrite the area equation to W = 24/L, by dividing both sides by L. Put this into the other equation so it reads: 10 = L + 24/L.
Subtract the 10 from both sides to leave the left side of the equation 0. The equation now reads: 0 = L + 24/L -- 10.
Remove the division in the problem. To simplify further, remove the L that is being divided into the 24 by multiplying both sides by L. This leaves the equation: 0 = L^2 + 24 -- 10L.
Use the quadratic equation to solve for L. The quadratic equation is found by factoring this equation. To factor, begin by writing two sets of parentheses each with an L as the first number within. After the L in each parenthesis there will be either a plus or minus sign and then a number. For example: 0 = (L + ?)(L - ?).
Find two numbers to fill in the blank spots. The two numbers must equal -- 10 when added and 24 when multiplied. In this case, a -- 6 and a -- 4 fit. The equation reads: 0 = (L -- 6)(L -- 4). This determines the answer to the question. The sides of the rectangle are 6 and 4.