How do you know that the perimeter of a rectangle is directly proportional to its length?

Answer 1

The perimeter of a rectangle is given by the formula P = 2(l + w). It is clear that as the length, l, increases, the perimeter, P, increases, as well. We say, therefore, that P is directly proportional to l. If l is the length and b is width of a rectangle then, the perimeter P of the rectangle is 2(l + b) units.

P = 2(l + b)

P = 2l + 2b If have b as a constant then, 2b will be a constant.

Now l is the varying quantity. Say 2b = K

P = 2l +K

Perimeter changes if the length of the rectangle changes. In particular, if the length increases the perimeter of the rectangle increases.

Similarly, if the length decreases the perimeter also decreases.

So, the perimeter is directly proportional to the length of the rectangle. Source: www.icoachmath.com

In the most simplest explanation, the sum of both lengths, and both widths of the rectangle, IS the perimeter. So obviously the perimeter is directly proportionate to its length (and its width).