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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.

Respuesta :

carlosego
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
calculista

Answer:

The area of the dilated rectangle is equal to [tex]28\ m^{2}[/tex]

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

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=7[/tex] ------> is an enlargement

[tex]y=(4/7)\ m^{2}[/tex]

substitute and solve for x

[tex]7^{2}=\frac{x}{(4/7)}[/tex]

[tex]x=49*(4/7)=28\ m^{2}[/tex]

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