Question

A rectangle with an area of 5/8 ft² is dilated by a factor of 8. What is the area of the dilated rectangle?

Answer 1

Answer:

The area of the dilated rectangle is equal to $40\ ft^{2}$

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

$z^{2}=\frac{x}{y}$

we have

$z=8$ ------> is an enlargement

$y=(5/8)\ ft^{2}$

substitute and solve for x

$8^{2}=\frac{x}{(5/8)}$

$x=64*(5/8)=40\ ft^{2}$

Answer 2

A dilation is basically a factor of enlargement or reduction, where you multiply the factor for the dilation. 

So,

Multiply the numerator 5 by the factor of 8. 

5*8= 40 

40/8 ft^2= 5 ft^2

The new area if 5 ft^2. 

I hope this helps!
~kaikers