Q1 of 18 Page 217

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

We know that area of equilateral triangle is given by a


Where s is the length of side.


Put s2 = q


Then


Here, is constant


When ‘q’ increases ‘a’ increases


When ‘q’ decreases ‘a’ decreases


So, ‘a’ is proportional to q. That means, ‘a’ is proportional to the square of the side


The constant of proportionality is .


More from this chapter

All 18 →
3

When a weight is suspended by a spring, the extension is proportional to the weight. Explain how this can be used to mark weights on a spring balance.

 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

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