Question

Ken is building a table. He attached planks of wood and now wants to build a border around the planks. The area of the entire table should be no larger than 3,276 square inches. All together, the planks are 36 inches wide and 72 inches long. Which quadratic equation represents the area of the planks and border combined? (The border must have equal width on each side.)

4x2 + 216x + 2,592 = 0

4x2 + 216x − 684 = 0

2x2 + 216x − 3,276 = 0

x2 + 108x + 3,276 = 0

Answer 1

let x be the width of the border

the

then the length is 72 + 2x
and the width is 36 + 2x

the area of the table plus the border is

\[(2x + 72)(2x + 36) = 4x^2 + 216x + 2592\]

then if the maximum area is to less than 3276

the equation becomes

\[4x^ 216x + 2592 = 3276\]