A rectangle has an area of open paren x squared minus 17 x plus 72 close paren square units. Since the area of a rectangle is determined using the formula, cap A is equal to l w , what could be the length and width of the rectangle?
Answer
A
length is equal to open paren x plus 12 close paren units and width is equal to open paren x plus 6 close paren units
B
length is equal to open paren x plus 9 close paren units and width is equal to open paren x plus 8 close paren units
C
length is equal to open paren x minus 6 close paren units and width is equal to open paren x minus 12 close paren units
D
length is equal to open paren x minus 8 close paren units and width is equal to open paren x minus 9 close paren units
Explanation
Factor the area expression by finding two numbers whose product is 72 and whose sum is −17. Those numbers are −8 and −9, so x² − 17x + 72 = (x − 8)(x − 9). Therefore, the rectangle could have length x − 8 units and width x − 9 units, which is choice D.
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