Question

A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's area?

Answer 1

A = l x w
Since 
l = 3w

Substitute the l with 3w
The formula will be

A = 3w + w
A = 4w

An example:
The given known values are: Length of 4 cm Width is unknown Perimeter is 34 cm Find the dimensions of the rectangle.   Since the geometric formula for perimeter is: 
P= 2 (l + w) 
L = 2w – 4 cm 
W =?   
Derivation and solution: 
34 = 2 (2w - 4) + 2w 
34 =  4w – 8 + 2w 
42 = 6w 42/6 = w 
W = 7 cm   

34 = 2l + 2(7) 
34 = 2l + 14 
2l = 34 – 14 
2l = 20 
L = 20/2 
L = 10 cm