Question

Find the area of rectangle of length and breadth. If length is doubled and breadth is halved find the area of new rectangle formed. Are the two areas equal​

Answer 1

Let l = the length of a rectangle.

Let w = the breadth or width of a rectangle.

The area A of a rectangle is given by the formula:

A = lw

Now, if the length l of a rectangle is doubled, then the new length is 2l. In addition, if the breadth or width w of a rectangle is reduced by half, then the new width is w - (1/2)w = (1)w - (1/2)w

= (2/2)w - (1/2)w

= [(2/2) - (1/2)]w

= [1/2]w

= w/2

To see how these changes in the length and in the width affect the area A of a rectangle, we substitute the new length and width into the area formula as follows:

A = 2l(w/2)

= (2/2)lw

= (1)lw

= lw

We now see that there is NO CHANGE in the area A of a rectangle if we double its length and also reduce its width by one-half.