A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign?

Answer 1

The areas of similar shapes are proportional to the square of their corresponding sides

area of banner : area of sign = 54^2 : 17^2
= 2916 : 289
= appr 10.1 : 1

OR, the long way ....

area of banner = 54x36 = 1944 inches^2

for the sign, we need the width
17/54 = w/36
w = 36(17/54) = 612/54 = 34/3

area of sign = 17(34/3) = 578/3

ratio of areas
= 1944 : 578/3
= 5832 : 578
= 2916 : 289 , same as above