Question

A rectangle with an area of

5/8 ft squared is dilated by a factor of 8.
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What is the area of the dilated rectangle?
Enter your answer in the box. Do not leave your answer as a fraction.
ft2

Answer 1

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

`Scale\ factor = 8\\\\Area\ of\ rectangle = (5)/(8)\ ft^2`

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)`

From given,

z = 8

`y = (5)/(8)`

Therefore,

`8^2 = (x)/((5)/(8))\\\\64 = x * (8)/(5)\\\\x = 8 * 5\\\\x = 40`

Thus the area of dilated rectangle is 40 square feet