+8262 A photograph of a painting measures 13 units by 17 units. If the scale factor is \(\frac{1}{3}\), what is the actual size of the painting?
WHAT DO I DO?
+129899 We have to assume that the actual painting is larger than the photo.
The area of the photo = 17 x 13 = 221sq units
The area of the actual painting - in square units - will be 221 x [ the scale factor]^2
And the scale factor = 3 so.....
221 x [3]^2 = 221 x 9 = 1989 square units
This makes sense........each dimension of the painting is 3 times that of the same dimension in the photo....so....if the area of the photo = L x W the area of the painting = 3L x 3L = 9[W x L]......9 times as much....!!!!
+2592 Treat the starting painting as X
1/3 is the scale factor
Put the orginal on top, in place of 1, and the outcome is the original paintings size
13/3 = 4.3333333333333333
17/3 = 5.6666666666666667
So the painting was originally 4.3 by 5.6 or 5.67 depending on how you round.
+129899 We have to assume that the actual painting is larger than the photo.
The area of the photo = 17 x 13 = 221sq units
The area of the actual painting - in square units - will be 221 x [ the scale factor]^2
And the scale factor = 3 so.....
221 x [3]^2 = 221 x 9 = 1989 square units
This makes sense........each dimension of the painting is 3 times that of the same dimension in the photo....so....if the area of the photo = L x W the area of the painting = 3L x 3L = 9[W x L]......9 times as much....!!!!
