Question

What happens to the area of a rectangle if you double the length of each of its four sides?  Explain how you determined your answer.

Answer 1

If you double the length of all 4 sides, the area is increased 4 times...

Let's try to prove it via some examples:

1. Let sides of a ractangle be 2 and 3 mt.

          So, the area (length x breadth) = 6 mt.

 

2. Let sides of a ractangle be 4 and 6 mt. (2x2 and 3x2)

          So, the area (length x breadth) = 24 mt.

 

3. Let sides of a ractangle be 8 and 12 mt. (4x2 and 6x2)

          So, the area (length x breadth) = 96 mt.

 

From example 1 and 2, we get

          24/6 = 4

And, example 2 and 3, we get

          96/24 = 4

 

Hence proved