Page 270 - ABCTE Study Guide_Neat

How is the area of a rectangle affected if both its length and width are doubled? Well, the area of a
parallelogram is given by the formula , where b is the base and h is the height.

We need to find a way to represent the doubled length and width. (Now’s a good time to note
that lengthand width and base and height may be used interchangeably. So the area of a parallelogram is
also given by the formula .)

If l is the length, then 2l is the doubled length. Similarly, if w is the width, then 2w is the doubled width.
Now just substitute the new length and new width into the formula where the old length and old width
were.

The new area is:

The old area was lw, and the new area is 4lw. That means that if the length and width are doubled, the
area is multiplied by four.

One more? How is the volume of a cone affected if the radius is doubled and the height is divided by two?
What are your initial thoughts? Do you think the volume will be affected?

The volume of a cone is given by the formula , where r is the radius of the base and h is the

height. The doubled radius can be represented by 2r and the halved height can be represented by . The
new volume is:

The old volume was , and the new volume is . The new volume is twice the old volume.

Question

How is the area of an isosceles right triangle affected if the length of each leg is doubled?

A The area is doubled.