Answer:
Ben's mistake was that he multiplied the area of the original triangle by the scale factor
Step-by-step explanation:
The complete question is
Beth enlarged the triangle below by a scale of 5. A triangle with a base of 4 centimeters and height of 3.5 centimeters. She found the area of the enlarged triangle. Her work is shown below.
1/2(4)(3.5)(5)= 35 cm2
What was Beth’s error?
we know that
The dilation is a non-rigid transformation that produce similar figures
so
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the enlarged triangle
y ----> the area of the original triangle
so
[tex]z^{2}=\frac{x}{y}\\x=y(z^2)[/tex]
The area of the enlarged triangle is equal to the area of the original triangle multiplied by the scale factor squared
[tex]x=\frac{1}{2}(4)(3.5)(5^2)=175\ cm^2[/tex]
therefore
Ben's mistake was that he multiplied the area of the original triangle by the scale factor
