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

The area of the dilated rectangle is equal to
`40\ ft^(2)`

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=8` ------> is an enlargement

`y=(5/8)\ ft^(2)`

substitute and solve for x

`8^(2)=(x)/((5/8))`

`x=64*(5/8)=40\ ft^(2)`