Answer :
Answer:
The ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.
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 [tex]x.[/tex]
So, 54 is equivalent to 36.
Thus, 17 is equivalent to [tex]x.[/tex]
[tex]\frac{54}{36} =\frac{17}{x}[/tex]
By cross multiplying we get:
[tex]54x=612[/tex]
Dividing both sides by 54 we get:
[tex]x=11.33\ inches.[/tex]
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.
= [tex]54\times 36:17\times 11.33[/tex]
= [tex]1944:192.61[/tex]
Therefore, the ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.
Answer:
The ratio of the area of the school banner to the area of the sign is 1944 : 192.61.
Step-by-step explanation:
Given:
Length of the School banner [tex](l_1)[/tex] = 54 inches
width of the school banner [tex](w_1)[/tex] = 36 inches
Length of the sign [tex](l_2)[/tex] = 17 inches
We need to find the ratio of the area of the school banner to the area of the sign
Solution:
First we will find the width of the sign.
Let the width of the sign be [tex]w_2[/tex]
Now we know that;
When two rectangles are similar to each other then their ratio of the dimension are equal.
so we can say that;
[tex]\frac{l_1}{l_2}=\frac{w_1}{w_2}\\\\\frac{54}{17}=\frac{36}{w_2}[/tex]
By using Cross multiplication we get;
[tex]w_2=\frac{17\times36}{54} = 11.33\ in[/tex]
Now we will find the Area.
Area of school banner is equal to length of the school banner times width of the school banner.
framing in equation form we get;
Area of school banner = [tex]54\times36 = 1944 \ ft^2[/tex]
Area of the sign is equal to length of the sign times width of the sign.
framing in equation form we get;
Area of the sign = [tex]17\times11.33= 192.61\ ft^2[/tex]
Now we will find the ratio of the area of the school banner to the area of the sign.
[tex]\frac{\textrm{Area of School Banner}}{\textrm{Area of the Sign}}=\frac{1944}{192.61}[/tex]
Hence The ratio of the area of the school banner to the area of the sign is 1944:192.61.