Question

A rectangular garden is four times as long as it is wide. Let w represent the width of the garden. Write two equivalent expressions that represent the area of the garden. Justify your answer.

Answer 1

Let's first determine the length.  If w is the width of the garden, and the length is 4 times the width, then l=4w.  Now, let's think of the area of a rectangle.  Area equals length times width (l*w) in a rectangle.  So, since l=4w, we can substitute 4w in for l: 4w*w.  That's one expression.  Now, let's make an equivalent expression.  4w is really 4*w, so we have 4*w*w.  w*w=w squared, so another equivalent expression is 4w^2.  (Note that ^2 means "squared.")

Answer: 4w*w, 4w^2