Question

Ken wants to build a table and put a border around it. The table and border must have an area of 3,276 square inches. The table is 36 inches wide and 72 inches long without the border. Which quadratic equation can be used to determine the thickness of the border, x?
4x^2 + 216x + 2,592 = 0
4x^2 + 216x − 684 = 0
2x^2 + 216x − 3,276 = 0
x^2 + 108x + 3,276 = 0

Answer 1

In this item, the table with the border that is to be constructed is in rectangular form. The area of the rectangle can be computed or solved by multiplying the length and the width. 

Since the given area is that of the table and border. If the thickness of the border is x then, the dimensions are as follow.
        width = 36 + 2x
        length = 72 + 2x

The area of the rectangle is calculated by multiplying the length and width.
           Area = length x width
            Area = (72 + x)(36 + x)
       3276 = 2592 + 108x + x²

Transpose all the terms on one side of the equation,
         x² + 108x - 684 = 0

Thus, the answer is not among the choices but that which is written above.