Ken wants to build a table and put a border around it. the table and border must have an area of 3,276 square feet.?
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?
4x2 + 216x + 2,592 = 0
4x2 + 216x - 684 = 0
2x2 + 216x - 3,276 = 0
x2 + 108x + 3,276 = 0

The border is 3 in wide along all edges of the table.

Step-by-step explanation:

You are told the total area is 3276 ft² and the dimensions of the table is 36 x 72 in

Either you really mean that the area is in in², or you have a huge border.

Presuming that the area is really in², adding in the border of "x" in makes the total length and width to be:

l = 72 + 2x

w = 36 + 2x

A = lw

3276= (72 + 2x)(36 + 2x)

3276 = 2592 + 216x + 4x²

subtracting 3276 from both sides:

4x² + 216x - 684 = 0

You would use the second of your four options to determine the length of the border.

Dividing both sides by 4:

x² + 54x - 171 = 0

completing the square:

x² + 54x = 171

x² + 54x + 729 = 171 + 729

(x + 27)² = 900

x + 27 = ± 30

x = -27 ± 30

Throwing out the negative number, our remaining x is:

x = 3

The border is 3 in wide along all edges of the table.

step-by-step explanation: