Question

If the length and width of a rectangle each change by a factor of nine, what happens to the area of the rectangle?

Answer 1

Answer:

The area of the rectangle changes by the factor of

$9^2$

Explanation:

Let l and w represent the length and width of the rectangle respectively.

The area is

A = lw

If these change by a factor of nine, then we have:

9l and 9w

The area, which is the product of the length and width becomes:

$\begin{gathered} A=9l\times9w \\ =9^2lw \\ =9^2A \end{gathered}$