Brunidad D.

asked • 12/22/15

A square with an area of 36 square inches is reduced to a square with an area of 9 square inches. What is the scale factor of this reduction?

Show your work.
What is the Scale Factor of this Reduction.

3 Answers By Expert Tutors

By:

Mark M. answered • 12/22/15

Tutor
5.0 (278)

Mathematics Teacher - NCLB Highly Qualified

Norbert J. M.

One-half (not two) is scale factor for the square side lengths
of the figures (6"x6" transformed reduction to 3"x3"), not
the areas (36in2 transformed reduction to 9in2).  
 
(1/2)2 = 1/4
Report

12/22/15

Kevin C.

tutor
Norbert, I agree with Mark.  The sides have the scale factor of 2 to 1, as Mark says.  In other words, the sides are in that ratio.  So the length of the original side is twice as long an the side of the reduced figure.
Report

12/22/15

Michael J.

I too agree with Mark.  After reading his solution and re-reading the question, the change in size of any shape is affected by the sides themselves.  The emphasis on area is not accurate in dilation because you can have two shapes that have different areas, but the length of one shape can be the same as the width of the second shape.  This also means that the width of one shape could be the same as the length of the second shape.  Because of this fact, the two shapes could be the same size based on the areas.
 
However, if both the length and width of one shape is larger or smaller than both the length and width of the second shape, then the change is size between the shape is clear to see.
Report

12/23/15

Norbert J. M.

Scale factor (C) is a value such that y=Cx.  Solve for "C."
Report

12/23/15

Norbert J. M. answered • 12/22/15

Tutor
5.0 (254)

Math / Structural Engineering

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.