Official Explanation
For all positive values of P, W, L, and A, consider the family of rectangles having perimeter P feet, width W feet, length L feet, and area A square feet.
In the first column of the table, select the expression in terms of P and W that is equivalent to A, and in the second column of the table select the expression in terms of P and W that is equivalent to L. Select only two expressions, one in each column.
Strategize
For any rectangle, A = LW, and P = 2L + 2W. Dividing both sides of the latter equation by 2 yields P/2 = L + W, and subtracting W from both sides yields \([\frac{P}{2} -W]\) = L. Therefore L = \([\frac{P}{2} -W]\) and
A = LW
= \((\frac{P}{2} -W)W\)
Alternatively, observe that, since A = LW, the expression for A is equivalent to the expression for L with an additional factor, W. And the only two expressions in the list that have this relationship are C, \((\frac{P}{2}-W)\), and E, \((\frac{P}{2} -W)W\)
RO1, A: Strategize
The correct answer is E, \((\frac{P}{2} -W)W\)
RO2, L: Strategize
The correct answer is C, \((\frac{P}{2} -W)\)
_________________