Question

You originally draw a design for an art contest on a 4 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar?

Answer 1

 as we know that If the 4" side of the card was scaled up to 10.5
 then the scaling factor is 10.5/4 = 2.625. 
The 5 side would  be the length 5 x 2.625 = 13.125 which exceeds the maximum dimension of 11. 

Thus, it is the 5 side which is scaled up to 10.5 and the scaling factor is therefore 10.5/5 = 2.1. 
The scaled up length of the 4 side is thus 4 x 2.1 = 8.4.