Question

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

Answer 1

you have to make a rectangle with the ratio 2:3 fit inside a rectangle with ratio 8:10.

we take the longest possible length for the length of the map and make it 10 inches.

since the width must then correspond such that the ratio of W:10 =2:3, W must be 2/3 of 10, or 6 2/3 inches.

so the largest possible dimensions are \[10\times6 \frac{ 2 }{ 3 }\]
or 66 2/3