Question

How do the areas of the triangles compare?

Original
3 in.
5 in.
4 in.
Area = 6 in.²

Scaled
15 in.
25 in.
20 in.
Area = 150 in.²

Answer 1

The area increased by a factor of 25, from 6 in^2 to 150 in^2, when the scale factor for the sides was 5.

Explanation:

The area increased from 6 in^2 to 150 in^2 when the Original triangle was scaled by a factor of 5 (in inches):

Original Scaled Factor

3 15 5

5 25 5

4 20 5

Area (in^2)

6 150 25

The larger increase in the sale factor for area is due to the area equation for a triangle: Area = (1/2)b*h. Since both the base and height both increase by a factor of 5, the are increses by a factor of 25:

Original: A = (1/2)b*h

Scaled by 5: A = (1/2)((5b)*(5h)) or (1/2)(25)(b*h) [(1/2)b*h is the original area)

Area(scaled) = 25*A(original)