A scale drawing of triangle XYZ

was created based on the scale factor of 0.5.
The scale drawing has two sides with a length of 3
and one side with a length of 4.245.

Which answer shows a scale drawing of triangle XYZ
with a scale factor of 3?

Responses

A triangle with two sides of length 2 & one side of length 2.83.© 2018 StrongMind. Created using GeoGebra.
Image with alt text: A triangle with two sides of length 2 & one side of length 2.83. © 2018 StrongMind. Created using GeoGebra.

A triangle with two sides of length 3 & one side of length 4.245.© 2018 StrongMind. Created using GeoGebra.
Image with alt text: A triangle with two sides of length 3 & one side of length 4.245. © 2018 StrongMind. Created using GeoGebra.

A triangle with two sides of length 18 & one side of length 25.47.© 2018 StrongMind. Created using GeoGebra.
Image with alt text: A triangle with two sides of length 18 & one side of length 25.47. © 2018 StrongMind. Created using GeoGebra.

A triangle with two sides of length 12 & one side of length 16.98.© 2018 StrongMind. Created using GeoGebra.

1 answer

To find the lengths of the sides of triangle XYZ based on the scale factor of 3, we first need to revert to the original dimensions of triangle XYZ before the initial scale factor of 0.5 was applied.

Each side of the scale drawing with lengths of 3 and 4.245 can be calculated back to the original side lengths by dividing by the scale factor of 0.5:

  • For the sides of length 3:
    • Original length = 3 / 0.5 = 6
  • For the side of length 4.245:
    • Original length = 4.245 / 0.5 = 8.49

So, the side lengths of the original triangle XYZ are approximately:

  • 6
  • 6 (assuming the other side that also had length 3 was the same)
  • 8.49

Now, we will scale up these sides by the new scale factor of 3:

  • New length of the two sides (each originally 6):
    • 6 * 3 = 18
  • New length of the side (originally 8.49):
    • 8.49 * 3 = 25.47

Therefore, the lengths of the sides of the triangle with a scale factor of 3 are:

  • Two sides of length 18
  • One side of length 25.47

Looking at the responses, the one that corresponds to this result is: A triangle with two sides of length 18 & one side of length 25.47.