Answer:
Length of poster is 9 inches and width of the poster is 3 inches.
Length of banner is 10 inches and width of the banner is 2 inches.
Step-by-step explanation:
Given:
Perimeter of Banner =24 in.
Perimeter of poster = 24 in.
we need to find the dimensions of poster and banner.
First we will find the dimension of poster.
Now Given:
A rectangular poster is 3 times as long as it is wide.
Let the Width of poster be
.
Length of the poster = ![3p](https://tex.z-dn.net/?f=3p)
Perimeter of poster = 24 in.
But perimeter of poster is equal to twice the sum of length and width.
framing in equation form we get;
![2(p+3p)=24\\\\2(4p)=24\\\\8p=24\\\\p=\frac{24}{8} = 3\ in.](https://tex.z-dn.net/?f=2%28p%2B3p%29%3D24%5C%5C%5C%5C2%284p%29%3D24%5C%5C%5C%5C8p%3D24%5C%5C%5C%5Cp%3D%5Cfrac%7B24%7D%7B8%7D%20%3D%203%5C%20in.)
Now width of poster = 3 inches
Length of the poster = ![3p = 3\times3 =9\ inches](https://tex.z-dn.net/?f=3p%20%3D%203%5Ctimes3%20%3D9%5C%20inches)
Hence Length of poster is 9 inches and width of the poster is 3 inches.
Now we will find the dimension of Banner.
Now Given:
A rectangular banner is 5 times as long as it is wide.
Let the Width of Banner be
.
Length of the banner = ![5b](https://tex.z-dn.net/?f=5b)
Perimeter of banner = 24 in.
But perimeter of banner is equal to twice the sum of length and width.
framing in equation form we get;
![2(b+5b)=24\\\\2(6b)=24\\\\12b=24\\\\b=\frac{24}{12} = 2\ in.](https://tex.z-dn.net/?f=2%28b%2B5b%29%3D24%5C%5C%5C%5C2%286b%29%3D24%5C%5C%5C%5C12b%3D24%5C%5C%5C%5Cb%3D%5Cfrac%7B24%7D%7B12%7D%20%3D%202%5C%20in.)
Now width of banner = 2 inches
Length of the banner = ![5b = 5\times2 = 10\ inches](https://tex.z-dn.net/?f=5b%20%3D%205%5Ctimes2%20%3D%2010%5C%20inches)
Hence Length of banner is 10 inches and width of the banner is 2 inches.