Farmer browns cornfield has an area of 12 sq yards what would be the lengths and widths?

Question

Word problem 

Answer 1

His field is a rectangle, and there's a formula for the area:

 

area = length times width, or

 

A = l*w (A is area, l is length, and w is width.  The * means to multiply).

 

The problem has a problem:  There is no limit to the combinations of length and width you can come up with that will give you an area of 12 sq yards.  In fact, if you choose any number at all for the length, you can find a number for the width that makes the area come out to 12.

 

So, let's just choose 4 for the length.  Our goal is to find a width which makes the area 12.  Let's start with our formula for the area, and then bring in the numbers we already have in mind.

 

A = l*w.  We know the area is 12, and the length is 4:

12 = 4*w.  Divide both sides by 4:

3 = w.

 

So we can choose a length of 4 yards, and a width of 3 yards.  Other combinations of length and width are 6 and 2, and 12 and 1.  Any two numbers whose product is 12 will work.