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.

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

The area of the enlarged triangle is equal to the area of the original triangle multiplied by the scale factor squared

therefore

Ben's mistake was that he multiplied the area of the original triangle by the scale factor

8(-10x+3.5y-7)

8×-10x + 8×3.5y + 8×-7

-80x + 28y - 56

therefore

-80x+28y-56 is the correct answer