Since the banner is in the shape of a rectangle, and we are asked to find the area of the banner, we are therefore asked to find the area of the rectangle.
The formula for an area of that shape is length multiplied by its width.
A = 144 = L * W
144 = L * W
The question doesn't specify what the length and width are. However, it does say that the width is 1/4 of the length, which means the length is 4 times larger than the width.
Let's say the width was "x".
If the length is 4 times larger than the width, then we can multiply the width, x, by 4. This will give length
L = 4 * x = 4x
Now we have values for both length and width:
L = 4x and W = x
Recall that the area of the rectangle is length times width, which means
A = 4x * x = 4x^2
But wait a minute, we already know what area is. It's 144.
144 = 4x^2
Simplify for x.
144/4 = (4x^2)/4
36 = x^2
x = 6
Width = x = 6 ft.
Length = 4x = 4(6) = 24 ft.