Question

A rectangle has a width of 5 yd and a length of 9 yd.

How does the area change when each dimension is multiplied by 4? The area is increased by a factor of 2.
The area is increased by a factor of 4.
The area is increased by a factor 8.
The area is increased by a factor 16.

Answer 1

Original area: 5X9=45
After you multiply the dimensions by 4 you get 5X4X9X4=720

720/45 = 16

The area is increased by a factor 16.

Answer 2

Option The area is increased by a factor of
`16`

Explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to scale factor squared

Let

z-----> the scale factor

x------> the area of the dilated rectangle

y------> the area of the original rectangle

`z^(2)=(x)/(y)`

we have

`z=4` ------> is an enlargement

so

substitute

`4^(2)=(x)/(y)`

`16=(x)/(y)`

`x=16y`

therefore

The area is increased by a factor of
`16`