Geometry...?

Question

You are reducing a map of dimensions 2 ft by 3 ft to fit to a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page?

a. 6 & 2/3 inch by 10 inch
b. 5 & 1/3 inch by 10 inch
c. 8 inch by 6 & 2/3 inch
d. 8 inch by 10 inch

Answer 1

this is a ratio problem.
consider the small edge. it was 24in, and is to be limited to 8 inches. thats a ration of 8/24 or 1/3.
consider the larger side. the ratio of reduction is 10/36 or 1/3.6.

so the larger side is the limiting factor. If you shrink the map by 1/3.6 the long side is 10 and the short side is 24/3.6, or 6.666, or 6 2/3.
so the correct answer is a, 6 & 2/3 x 10