7
QuizMultiple Choice

Modeling with Functions — Quiz

Question 7 • Mathematics III

A rectangle with constant area has possible lengths and widths as shown in the table. Width vs. Length of a Rectangle Width w Length l 2 37 point 5 4 18 point 7 5 6 12 point 5 8 9 point 3 7 5 Which equation can be used to find any corresponding length and width that fit the pattern in this table?

Answer
A
l is equal to k over w , where l is the length, w is the width, and k is a constant open paren w is not equal to 0 close paren
B
l is equal to k w raised to the 1 half power , where l is the length, w is the width, and k is a constant
C
l is equal to m w plus b , where l is the length, w is the width, and m and b are constants
D
l is equal to A w squared , where l is the length, w is the width, and A is a constant

Explanation

For a rectangle with constant area, length × width stays constant. The table follows this inverse relationship: for example, 2 × 37.5 = 75 and 6 × 12.5 = 75. So the length can be found with l = k/w, where k is the constant area; choice A gives this equation.

AI-written and checked against the verified answer.

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