Question

Find the area of a square with side a when a=2 in, a=12 in, and a=0.8 in. Are the area of a square and the length of its side directly proportional quantities? Why or why not?

Answer 1

They are directly proportional quantities.

Explanation:

DEFINITION

Two quantities are said to be directly proportional if an increase in one quantity lead to an increase in the other quantity.

Area of a Square =
`Length^2`

Area of a Square of Length 2 inch =
`2^2=4 \:square \:inch`

Area of a Square of Length 12 inch =
`12^2=144 \:square \:inch`

Area of a Square of Length 0.8 inch =
`0.8^2=0.64 \:square \:inch`

Arranging the sides and corresponding area in ascending order:

(0.8, 2, 12) = (0.64, 4, 144)

We notice that as the length increases, the area also increases.

Therefore, the area of a square and the length of its side are directly proportional quantities.

Answer 2

4 inches²

144 inches²

0.64 inches²

Yes, the area of a square and the length of its side directly proportional quantities.

Explanation:

In this question, we have to find the area of square by changing the lengths of a side. Given lengths are: 2, 12, 0.8. I will evaluate the area of each side and try to find out the relation between area and length of side.

First, we start with the smallest length (a=0.8 inches)

Area of a square is calculated by taking the square of single side (since both sides are equal).

Area of square = a²

Area of square = 0.8²

Area of square = 0.64 inches²

Area of square with smallest side length (a=0.8 inches) = 0.64 inches²

Secondly, we start with the 2nd highest length (a=2 inches)

Area of square = a²

Area of square = 2²

Area of square = 4 inches²

Area of square with second largest side length (a=2 inches) = 4 inches²

Thirdly, we start with the highest length (a=12 inches)

Area of square = a²

Area of square = 12²

Area of square = 144 inches²

Area of square with highest side length (a=12 inches) =144 inches²

As we can see, with the increase in the length of a side, area of square is also increasing. Therefore, yes the area of a square and the length of its side are directly proportional quantities as the area increases or decreases when the length of the side increases or decreases.