Draw two triangles that look similar and label them as QRS and TUV. Label the sides of both triangles with numerical values such that the triangles are, in fact, similar with a scale factor of 5/2.

Answer 1

Here's a description of how to create two similar triangles, QRS and TUV, with numerical values that reflect a scale factor of \(\frac{5}{2}\).

1. Triangle QRS:

   • Let the lengths of the sides of triangle QRS be:
     • QR = 4
     • RS = 3
     • SQ = 5

2. Triangle TUV:

   • To maintain the scale factor of \(\frac{5}{2}\), we multiply each side of triangle QRS by \(\frac{5}{2}\):
     • TU = \(4 \times \frac{5}{2} = 10\)
     • UV = \(3 \times \frac{5}{2} = 7.5\)
     • VT = \(5 \times \frac{5}{2} = 12.5\)

Now, the two triangles can be depicted as follows:

Triangle QRS:
      R
     / \
    /   \
  Q/_____\S
     4  
    3   5

Triangle TUV:
       U
      / \
     /   \
   T/_____\V
      10  
    7.5  12.5

Labeling:

• Triangle QRS:

  • Side QR = 4
  • Side RS = 3
  • Side SQ = 5

• Triangle TUV:

  • Side TU = 10
  • Side UV = 7.5
  • Side VT = 12.5

These triangles are similar with a scale factor of \(\frac{5}{2}\), as proven by the proportionality of their corresponding side lengths.