Answer:
Yes they are directly proportional quantities.
Step-by-step explanation:
We find the area of a square by;
A = length squared or (L)² , where 'L' stands for length and 'A' stands for area.
So Area = L²
Assume the length is a units and increase the length by 2 units
The initial area before increasing the length is a²
After increasing the length, the area becomes: (a + 2)² = a² + 4a + 4
Now we subtract the initial area from the final area and get;
(a² + 4a + 4) - a² = 4a + 4
So the new area increases by 4a + 4 units.
Hence, the area increases as the length increases implying that the area of a square is directly proportional to its length.
We denote this proportionality as;
A ∝ L
