The area of dilated rectangle is 40 square feet
Solution:
Given that,
A rectangle with an area of 5/8 ft squared is dilated by a factor of 8
[tex]Scale\ factor = 8\\\\Area\ of\ rectangle = \frac{5}{8}\ ft^2[/tex]
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]
From given,
z = 8
[tex]y = \frac{5}{8}[/tex]
Therefore,
[tex]8^2 = \frac{x}{\frac{5}{8}}\\\\64 = x \times \frac{8}{5}\\\\x = 8 \times 5\\\\x = 40[/tex]
Thus the area of dilated rectangle is 40 square feet
