Question

A rectangle has a width of 9 km and a length of 6 km. How does the area change when each dimension is multiplied by 3?

Answer 1

The area of the rectangle increases by a factor of 9

Answer 2

For this case we have that by definition the area of a rectangle is given by:

$A = wl$

Where

• w: width of the rectangle
• l: length of the rectangle

The area of the original rectangle is given by:

$A1 = (9) (6)\\A1 = 54$

The area of the new rectangle is given by:

$A2 = (3 * 9) (3 * 6)\\A2 = 9 * (9) (6)\\A2 = 9 * 54\\A2 = 9 * A1$

Therefore, the original area increases with a factor of 9.

Anwer:

the original area increases by a factor of 9.

$A2 = 9 * A1$