Question

In the diagram above, rectangles DEFG and WXYZ are similar. The ratio of the area of DEFG to WYXZ is 1:4. A student's work to find ZY is shown below. Describe and correct the error in finding ZY.

Answer 1

Was the 12 of GF given??
The area ratio should be 1:4, so if l×w = area (a) of DEFG, then L×W = Area (A) of WXYZ.
Since 4:1 is 4×1, A = 4×a or 4a
Since GF is length (l) and is 12, we can say that 12w = a
12×4 = 48 for length of ZY (L), and WX is also 48, and to find W would be: 48W = A
48W = 4a, since A=4a
Not sure what else you want by the limited information given!

Answer 2

The right answer is

The ratio of the corresponding sides is not 1:4; the ratio is 1:2. Therefore, you should multiply 2 times 12 to get the correct answer of ZY = 24.