Answer:
The area of the dilated rectangle is \(28\ m^{2}\)
Step-by-step 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
\(z^{2}=\frac{x}{y}\)
In this problem we have
\(z=7\)
\(y=(4/7)\ m^{2}\)
substitute and solve for x
\(7^{2}=\frac{x}{4/7}\)
\(x=49*(4/7)=28\ m^{2}\)
