Question

A rectangle with constant area has possible lengths and widths as shown in the table below.

Width vs. Length of a Rectangle
Width (w)
Length (l)
2
37.5
4
18.75
6
12.5
8
9.375

Which equation can be used to find any corresponding length and width that fit the pattern in this table?
l = StartFraction k Over w EndFraction, where l is the length, w is the width, and k is a constant (w not-equals 0)
l = m w + b, where l is the length, w is the width, and m and b are constants
l = k w Superscript one-half, where l is the length, w is the width, and k is a constant
l = a w squared, where l is the length, w is the width, and a is a constant

Answer 1

The first equation: l = k/w.

Reason: Constant area means w·l = A (constant), so l = A/w. From the table w·l = 2·37.5 = 75, 4·18.75 = 75, etc., so l = 75/w (w ≠ 0). The other forms (linear, square-root, quadratic) do not match reciprocal variation.