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Levart [38]
3 years ago
12

Brice wants to build a table and put a border around it. The table and border must have an area of 3,006 square inches. The tabl

e 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?
A. 4x2 + 216x + 2,592 = 0

B. 4x2 + 216x − 414 = 0

C. 2x2 + 216x − 3,004 = 0

D. x2 + 108x + 2,592 = 0
Mathematics
1 answer:
SVEN [57.7K]3 years ago
8 0
B is the correct answer.

We are adding the border of x thickness to all 4 sides of the table.  This makes the new width of the table 36+x+x = 36+2x and the new length of the table 72+x+x=72+2x.  To find the area, we multiply the length and width:

(36+2x)(72+2x) = 3006

Multiplying the binomials, we get:
36*72 + 36*2x + 2x*72 + 2x*2x = 3006
2592 + 72x + 144x + 4x² = 3006

Combining like terms gets us
2592 + 216x + 4x² = 3006

Subtract 3006 from both sides:
2592 + 216x + 4x² - 3006 = 3006 - 3006
-414 + 216x + 4x² = 0

Writing in standard form we have
4x²+216x-414=0
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