Answer:
The friend's claim is incorrect
if you dilate the pictured rectangle by a scale factor of three, then the area of your new rectangle will be 9 times the original area
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor, and the ratio of its areas is equal to the scale factor squared
so
In this problem, the friend's claim is incorrect
The scale factor is 3
The scale factor squared is 3^2=9
so
if you dilate the pictured rectangle by a scale factor of three, then the area of your new rectangle will be 9 times the original area
Verify
The dimensions of the original rectangle ABCD are
AB=6 unis
BC=4 units
The original area is
A=(6)(4)=24 units^2
If the scale factor is 3
The new dimensions are
A'B'=6*3=18 unis
B"C'=4*3=12 units
The new area is
A'=(18)(12)=216 units^2
Divide the areas
216/24=9
therefore
The new area is 9 times the original area
