A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? cap v is equal to l w h cap p is equal to 2 times open paren l plus w close paren
Answer
A
y is equal to 5 open paren 28 minus 2 x close paren x
B
y is equal to 5 open paren 14 minus x close paren x
C
y is equal to 5 open paren 14 minus 2 x close paren x
D
y is equal to 5 open paren 28 minus x close paren x
Explanation
Let the base dimensions be x and w. The perimeter condition gives 2(x + w) = 28, so x + w = 14 and w = 14 − x. The volume is base area times height: V = xw(5) = 5x(14 − x), which matches choice A.
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