Answer:
The ratio of the area of the school banner to the area of the sign is <u>1944 cubic inches : 192.61 cubic inches.</u>
Step-by-step explanation:
Given:
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.
Now, to find the ratio of the area of the school banner to the area of the sign.
Dimensions of school banner :
Length = 54 inches.
Width = 36 inches.
Dimension of school sign:
Length = 17 inches.
So, to we find the width of sign by using cross multiplication method:
Let the width be ![x.](https://tex.z-dn.net/?f=x.)
So, 54 is equivalent to 36.
Thus, 17 is equivalent to ![x.](https://tex.z-dn.net/?f=x.)
![\frac{54}{36} =\frac{17}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B54%7D%7B36%7D%20%3D%5Cfrac%7B17%7D%7Bx%7D)
By cross multiplying we get:
![54x=612](https://tex.z-dn.net/?f=54x%3D612)
Dividing both sides by 54 we get:
![x=11.33\ inches.](https://tex.z-dn.net/?f=x%3D11.33%5C%20inches.)
Thus, the width of sign = 11.33 inches.
Now, to get the ratio of the area of the school banner to the area of the sign:
Area of the school banner : Area of the school sign.
= ![54\times 36:17\times 11.33](https://tex.z-dn.net/?f=54%5Ctimes%2036%3A17%5Ctimes%2011.33)
= ![1944:192.61](https://tex.z-dn.net/?f=1944%3A192.61)
Therefore, the ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.