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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.

Respuesta :

Leader
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.
calculista

Answer:

Option The area is increased by a factor of [tex]16[/tex]

Step-by-step 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

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=4[/tex] ------> is an enlargement

so

substitute

[tex]4^{2}=\frac{x}{y}[/tex]

[tex]16=\frac{x}{y}[/tex]

[tex]x=16y[/tex]

therefore

The area is increased by a factor of [tex]16[/tex]


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