The explanation behind the area of a rectangle increases by a factor of 4 when the side length is doubled is due to the fact that;
The length and width are double which translates to a product of 4 which means the area will increase by a factor of 4.
We know that area of a rectangle is;
A = length x width
Now, let us say we have a sample rectangle with length of 7 cm and width of 3 cm.
This means area is; A = 7 x 3 = 21 cm²
Now, if we double the side lengths, it means our length is now 7 x 2 = 14 cm² and width now 3 x 2 = 6
Our new area is now 14 x 6 = 84 cm²
If we look at the initial area we will see that it has been increased by a factor of 4 to obtain 84.
- The reason behind this is due to the fact the length and width are double which translates to a product of 4 which means the area will increase by a factor of 4.
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