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?

Let the area of rectangle be a, length of the rectangle be x and breadth be y.

Then the area of rectangle = Length × breadth

⇒ a = x × y

⇒ a = xy

Area is given as 1m², which is constant.

⇒ xy = 1

This is the algebraic equation which gives the relation between length and breadth of a rectangle whose area is 1m².

Now we see if there is any proportionality between length and breadth

We have xy = 1. So, length or breadth increases, the other decreases.

Also, if length or breadth decreases, the other increases

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

We can write:

⇒

So, length is proportional to the reciprocal of the breadth.

That means, length and width are inversely proportional.

The constant of proportionality is 1.