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? (2 points) Question 1 options: 1) 4x2 + 216x + 2,592 = 0 2) 4x2 + 216x − 684 = 0 3) 2x2 + 216x − 3,276 = 0 4) x2 + 108x + 3,276 = 0

Answer 1

A=(36+2x)(72+2x), and we are told that this area is 3276 so

4x^2+216x+2592=3276 subtract 3276 from both sides

4x^2+216x-684=0

Answer 2

4x^2+216x-684=0

Explanation:

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.

LEt x be the border around it

Length of the table and border becomes (72+x+x)

Width of the table and border becomes (36+x+x)

The table and border must have an area of 3,276 square inches.

ARea of the rectangle = Length * width

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

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

3276=2592+216x+4x^2

Subtract 3276 from both sides

4x^2+216x-684=0