Question

The area of a rectangle depends on its length and width. For the area to remain constant, the length varies inversely with the width, and vice versa. If the area is 475, width is ( w ), and length is ( l ), which equation represents this inverse variation?

a) ( lw = 475 )
b) ( l = 475/w )
c) ( l = 475w )
d) ( lw^2 = 475 )

Answer 1

The equation that represents the inverse variation between the length and width of a rectangle, given a constant area of 475, is l = 475/w.

Step-by-step explanation:

The area of a rectangle is calculated by multiplying its length (l) by its width (w). When the length varies inversely with the width to keep the area constant, it means that as the width increases, the length decreases proportionally, so the product of the two remains the same. Since the area is given as 475, the correct equation to represent this inverse variation is l = 475/w, where l is the length and w is the width of the rectangle. If we multiply both sides of this equation by w, we get lw = 475, which also represents the constant area of the rectangle.