Answer:
The ratio of the area of the school banner to the area of the sign is 256 : 25
Step-by-step explanation:
The school banner has a length of 48 inches and a width of 30 inches.
Suppose, the width of the sign is [tex]x[/tex] inch.
Given that, the sign is similar to the school banner and has a length of 15 inches.
So, according to the ratio of length and width, the equation will be......
[tex]\frac{48}{30}= \frac{15}{x} \\ \\ 48x=30*15=450\\ \\ x=\frac{450}{48}=9.375[/tex]
So, the width of the sign is 9.375 inches.
Formula for area of rectangle is: [tex](length\times width)[/tex]
So, the area of the school banner [tex]=(48\times 30)inch^2= 1440 inch^2[/tex]
and the area of the sign [tex]=(15\times 9.375)inch^2 = 140.625 inch^2[/tex]
Thus, the ratio of the area of the school banner to the area of the sign will be: [tex]\frac{1440}{140.625}= \frac{256}{25}=256:25[/tex]
