Question

A rectangle has an area of 48 in^2. Every dimension of the rectangleis multiplied by a scale factor, and the new rectangle has an area of 12 in^2. What is the scale factor?

Answer 1

Let the dimensions of the first rectangle be L and W.  Then L*W = 48 in^2.

If we multiply both dimensions of this first rectangle by scale factor f, we get

f*L * f^W = 12 in^2.  Our job is to determine the scale factor, f.

Note that f^2*L*W = 12 in^2, and that LW = 48 in^2.

Therefore, the above equation becomes f^2*(48 in^2) = 12 in^2.

Dividing both sides by (48 in^2), we get f^2 = 1/4.

Solving for the scale factor, we get f = √(1/4) = 1/2.

The scale factor is 1/2.