Question

A rectangle with an area of 47 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
`28\ m^(2)`

Explanation:

we know that

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

Let

z------> the scale factor

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

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

so

`z^(2)=(x)/(y)`

In this problem we have

`z=7`

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

substitute and solve for x

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

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

Answer 2

Area of rectangle = lb = 47 m^2

Dilation by a factor of 7 results in 1/7 l x 1/7 b = 1/49 lb = 1/49 (47) = 47/49 = 0.9592