Question

Lisa wants to build a table and put a border around it. The table and border must have an area of 3,996 square inches. The table is 42 inches wide and 36 inches long without the border. Which quadratic equation can be used to determine the thickness of the border, x? 4x2 + 156x − 2,484 = 0 4x2 + 156x − 3,024 = 0 2x2 + 156x − 3,996 = 0 x2 + 78x + 3,996 = 0

Answer 1

4x^2 + 156x - 1512 = 0

Explanation:

To determine the thickness of the border, we need to find the quadratic equation that represents the problem. The area of the table and border is the product of the width and length:

Area = (42 + 2x)(36 + 2x)

Expanding the expression, we get:

Area = 4236 + 2x36 + 2x42 + 2x2x

Simplifying further:

Area = 1512 + 72x + 84x + 4x^2

Area = 4x^2 + 156x + 1512

Comparing this equation to the given options, we see that:

4x^2 + 156x - 1512 = 0

Answer 2

The table and border must have an area of 3,996 square inches. The table is 42 inches wide and 36 inches long without the border. To find the ...
Top answer · 53 votes
Option AThe quadratic equation can be used to determine the thickness of the border, x is