A rectangle has a width of 2.45 feet and a length of 6.5 feet. How will the area of the rectangle change if each side is increased by a factor of 5?

Question

A rectangle has a width of 2.45 feet and a length of 6.5 feet. How will the area of the rectangle change if each side is increased by a factor of 5?

Answer 1

To answer this question, you need to remember two things. First, what is the formula to find a rectangle? Second, what is a "factor"?

 

Let's start by answering the second thing first, what is a "factor"? Technically, a "factor" in any math problem is a number (or sometimes numbers contained in parenthesis) that is part of a multiplication problem.  I like to remember it like the saying "X-Factor". That way I remember X (as in multiplication) is connected with the word "factor". It's corny, I know, but it helps stick in my head. 

 

Okay, so now we know that "factor" means multiplication, we can answer "each side is increased by a factor of 5" by simply multiplying each number by 5.

 

Rectangle's WIDTH times a factor of 5 = ____

2.45 ft x 5 = 12.25 ft

 

Rectangle's LENGTH times a factor of 5 = ____

6.5 ft x 5 = 32.5 ft

 

This step is complete.

 

Now that you have the new measurements for the rectangle's length and width (32.5 ft and 12.25 feet, respectively). So now you need to remember the formula for a rectangle, length times width. This is now another multiplication problem from here:

 

Rectangle's new LENGTH x Rectangle's new WIDTH = Rectangle's AREA (after length and width is increased by a factor of 5)

32.5 ft x 12.25 ft = ______ square feet

 

(I'll leave the final step to you, but I hope this helps explain how you got to the answer.)

 

Answer 2

The ratio of the areas of two similar figure is the same as the square of the scaling factor.

The scaling factor here is 5, so the larger figure is 25 times the area of the smaller.