Question

Are the area of a square and the length of its side directly proportional quantities?

Answer 1

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