Question

A rectangular picture has dimensions 2 1/2 by 1 1/2. It is to be enlarged so that it is still similar to the original rectangle. If the longer dimension is now 10 , how much longer than the original is the perimeter now

Answer 1

The original perimeter is:
p = 2 (w) +2 (l)
First we look for the scale factor of the longest dimension, which is given by:
k = (10) / (2 1/2)
k = 4
Then, the perimeter is given by:
p '= 2 (4w) +2 (4l)
Rewriting:
p '= 4 (2 (w) +2 (l))
p '= 4p
Answer:
the perimeter now is 4 times longer than the original