Q1 of 18 Page 217

For squares, is area proportional to square of the length of a side? If so, what is the constant of proportionality?

Let us consider a square of side ‘s’ and its area ‘a’


Let s = 1cm


Area = (side)2


∴ a = 1 × 1 = 1cm2


Now, let us change the side and see how it affects the area:


Let s = 2 cm, now a = (2)2 = 4 cm2


Let s = 2.25 cm, now a = (2.25)2 = 5.0625 cm2


Let s = 3 cm, now a = (3)2 = 9 cm2


Let s = 0.4 cm, now a = (0.4)2 = 0.16 cm2


Now we will write the above result in a tabular form, and calculate a/s ratio in each case:



From the table, we can see that a/s ratio is not a constant. We will not get ‘a’ by multiplying ‘s’ by a fixed number. So, a is not proportional to s.


More from this chapter

All 18 →
4

In the angle shown below, for different points on the slanted line, as the distance from the vertex of the angle changes, the height from the horizontal line also changes.


i) Prove that height is proportional to the distance.


ii) Calculate the constant of proportionality for 30°, 35° and 60° angles.

 1

Prove that for equilateral triangles, area is proportional to the square of the length of a side. What is the constant of proportionality?

 2

In rectangles of area one square metre, as the length of one side changes, so does the length of the other side. Write the relation between the lengths as an algebraic equation. How do we say this in the language of proportions?

 3

In triangles of the same area, how do we say the relation between the length of the longest side and the length of the perpendicular from the opposite vertex? What if we take the length of the shortest side instead?