This type of problem is a frequent flyer on the questions board! To do this problem, first set up your variables, and identify the area equation for a rectangle; a bulletin board is usually a rectangle.
A = L * W (the * means "times")
A = area
L = length
W = width
Now, use the information in the problem to specify length in terms of width. Here's how:
You know the length (L) is 3 feet less than four times the width. Four times the width is 4W. You need to subtract 3 feet from this to get the length. So:
L = 4W - 3
Now, plug your information into the equation, using the given area = 52 square feet:
52 = (4W-3) * W
Multiply the right side out using distribution:
52 = 4W^2 - 3W (the ^2 means "squared")
Subtract 52 from both sides:
0 = 4W^2 - 3W - 52
I will let you finish this... it is now a factoring problem. Use any factoring method you like.
Note: You will get two answers for W. One answer will be negative and will therefore be invalid, because you cannot have negative lengths. Use the positive answer for W to substitute into the length equation (L = 4W - 3) to get length.
Check your answer to assure that when you multiply L * W you do get 52. ALWAYS CHECK YOUR ANSWER!! :-)