Answer :
Let t be the thickness of the border. Adding the border to all side of the table will increase the length and the width by 2t. The area of a rectangle is the product of the length and width. With the addition of the thickness of the border, the new quadratic equation becomes,
(36 + 2t)(72 + 2t) = 3,276.
(36 + 2t)(72 + 2t) = 3,276.
Answer:
[tex]4\cdot x^{2} + 18\cdot x -3258\,ft^{2} = 0[/tex], [tex]x \approx 26.378\,ft[/tex]
Step-by-step explanation:
The area of the table and border can be computed by using the following second order-polynomial:
[tex]3276\,ft^{2} = (2\cdot x + \frac{36}{12}\,ft )\cdot (2\cdot x + \frac{72}{12}\,ft )[/tex]
[tex]3276\,ft^{2} = (2\cdot x + 3\,ft)\cdot (2\cdot x + 6\,ft)[/tex]
The thickness of the border can be determined by expanding and simplyfiying the algebraic expression:
[tex]3276\,ft^{2} = (2\cdot x)^{2} + 9\cdot (2\cdot x) + 18\,ft^{2}[/tex]
[tex]4\cdot x^{2} + 18\cdot x -3258\,ft^{2} = 0[/tex]
The roots of the polynomial are:
[tex]x_{1} \approx 26.378\,ft[/tex] and [tex]x_{2} \approx -30.878\,ft[/tex]
Knowing that length is a positive unit, the first root is the only solution that is reasonable:
[tex]x \approx 26.378\,ft[/tex]