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