Q3 of 18 Page 217

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?

Let us consider triangles of same area.


That means area is constant. Let it be ‘a’.


Let the length of the longest side be x and length of the perpendicular from the opposite vertex to this longest side be y.


Then we have,


⇒


⇒ xy = 2a


Here 2a is constant. So, if x or y increases, the other decreases.


Also, if x or y decreases, the other increases.


Their product will remain constant only if this simultaneous increase and decrease take place.


We can write:


⇒


So, x is inversely proportional to y


If we change the shape of the triangle while keeping the area the same, the longest side that we considered may become the shortest side. Then y should increase proportionately so that area will remain the same.


More from this chapter

All 18 →
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?

 4

In regular polygons, what is the relation between the number of sides and the degree measure of an internal angle? Can it be stated in terms of proportion?

 5

A fixed volume of water is to flow into a rectangular water tank. The rate of flow can be changed by using different pipes. Write the relations between the following quantities as an algebraic equation and in terms of proportions.

i) The rate of water flow and the height of the water level.


ii) The rate of water flow and the time taken to fill the tank.