Question

A rectangle with an area of 4/7 m² is dilated by a factor of 7. What is the area of the dilated rectangle? Do not leave your answer as a fraction.

Answer 1

The area of the dilated rectangle is equal to
`28\ m^(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=7` ------> is an enlargement

`y=(4/7)\ m^(2)`

substitute and solve for x

`7^(2)=(x)/((4/7))`

`x=49*(4/7)=28\ m^(2)`

Answer 2

The area is increased by a square of the scale factor
Calculating the area we have:
(4/7)*7^2 =
(4/7)*49
(49/7)*4 =
7*4=
28 m^2
answer:
the area of the dilated rectangle is 28 m ^ 2