If the width of a rectangle is doubled, how does it affect the area?

To understand how doubling the width of a rectangle affects its area, we first need to look at the formula for the area of a rectangle, which is calculated as the product of its width and height:

Area = width × height.

Let’s say the original width of the rectangle is represented by ( w ) and the height by ( h ). Therefore, the area can be expressed as:

Area = ( w \times h ).

Now, if the width of the rectangle is doubled, the new width becomes ( 2w ). The area of the rectangle with this new width will now be:

New Area = ( (2w) \times h ).

By simplifying this expression, we find:

New Area = ( 2w \times h = 2(w \times h) ).

This shows that the new area is indeed twice the original area. Thus, when the width of the rectangle is doubled, the area doubles as well. The reason for this is linked to the direct relationship between one dimension (width) of the rectangle and its overall area, which is fundamentally dependent on multiplying the width by the height. This relationship holds regardless of the specific height, provided it remains constant.