Use the scale factor to find the area of the enlarged figure. Explain your steps. A small rectangle has a length of 8 and width of 4. A large rectangle has a length of 25.6 and width of a.

9514 1404 393

  327.68 units^2

Step-by-step explanation:

The area of the small figure is ...

  area = length · width

  area = (8)(4) = 32 . . . . square units

The scale factor is ...

  scale factor = large length / small length = 25.6/8 = 3.2

The area of the larger rectangle will be the small rectangle area multiplied by the square of the scale factor:

  (32 units^2)(3.2^2) = 327.68 units^2

Additional comment

We note the width is half the length, so we could figure the larger rectangle's width at 25.6/2 = 12.8 units. Then its area would be

  length · width = (25.6 units)(12.8 units) = 327.68 units^2

This seems easier to me, but is not the method required by the problem statement.

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.