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A rectangle with an area of 8 ft² is dilated by a factor of 4. What is the area of the dilated rectangle?

1) 12 ft

2) 32 ft

3) 64 ft

4) 128 ft

Verified Answer :

calculista

Answer:

Option 4) \(128\ ft^{2}\)

Step-by-step explanation:

we know that

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

Let

z------> the scale factor

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

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

so

\(z^{2}=\frac{x}{y}\)

we have

\(z=4\)

\(y=8\ ft^{2}\)

substitute and solve for x

\(4^{2}=\frac{x}{8}\)

\(x=16(8)=128\ ft^{2}\)

he required area of dilated rectangle is x = 128ft.

Given that,

The area of a rectangle = 8 ft²,

And its dilated with factor of 4 .

We have to find ,

Area of the dilated rectangle.

According to the question,

The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object).

When the absolute value of the scale factor is greater than one, an expansion occurs.

Let, z the scale factor,


x the area of the dilated rectangle,


y the area of the original rectangle,

Scale factor(z) = Dimension of the new shape(x)  ÷ Dimension of the original shape(y).

Then ,

\(z^{2} = \frac{x}{y} \\(4)^{2} = \frac{x}{8} \\16 = \frac{x}{8} \\x = (16).(8) \\x = 128\\\)

Hence , The required area of dilated rectangle is x = 128ft.

For more information about Dilated factor click the link given below.

https://brainly.com/question/18220282

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