measure the trees to the nearest half inch tree a is one inch ,tree two is one and a half inches , find the scale factor

Question

need to know what the scale factor is measuring the two trees to the nearest half inch,tree A) is one inch.,tree B)is one and a half inches. what would be the scale factor.

Answer 1

Carl,

 

The scale factor is the simply ratio of the two measurements.  Specifically it is the ratio of the second height divided by the first height.  

 

Height1 = H1 = 1 inch = 1"

Height2 = H2 = 1-1/2 inches = 1.5"

 

H2 / H1 = 1.5" / 1" =1.5

 

So 1.5 is the scale factor.  It is the number you have to multiply Height1 by (or scale it by) to get Height2.  In this case the second object is larger than the first object so the scale factor is greater than one, but if the second object is smaller the scale factor would be less than one.

Answer 2

Carl, the scale factor is what you multiply one measurement by to get the 2nd.

 

In other words, 2 1/2, or 5/2 x ? = 1

 

Anything times its reciprocal gives us one, so the scale factor for A is 2/5.

 

5/2 x ? = 3/2

 

Now, we have to divide.  3/2 ÷ 5/2 = 3/2 x 2/5 = 6/10 = 3/5.  We always put the scale factor into lowest terms.

 

So, A is 2/5 and B is 3/5

 

Let's check.  5/2 x 2/5 = 10/10 = 1

 

5/2 x 3/5 = 15/10 = 1 1/2.  Check!