The side lengths for triangles DEF, GHI, and JKL, obtained by applying the respective scale factors to the sides of triangle ABC, are recorded in the table as follows:
Triangle | Scale Factor | Short Side | Medium Side | Long Side
ABC | 1 | 4 | 5 | 7
DEF | 2 | 8 | 10 | 14
GHI | 3 | 12 | 15 | 21
JKL | 1/2 | 2 | 2.5 | 3.5
To find the side lengths of triangles DEF, GHI, and JKL, we'll use the given scale factors for the dilations relative to triangle ABC.
Triangle DEF (Scale Factor = 2):
Length of the short side (DE): 4 * 2 = 8
Length of the medium side (EF): 5 * 2 = 10
Length of the long side (DF): 7 * 2 = 14
Triangle GHI (Scale Factor = 3):
Length of the short side (GH): 4 * 3 = 12
Length of the medium side (HI): 5 * 3 = 15
Length of the long side (GI): 7 * 3 = 21
Triangle JKL (Scale Factor = 1/2):
Length of the short side (JK): 4 * 1/2 = 2
Length of the medium side (KL): 5 * 1/2 = 2.5
Length of the long side (JL): 7 * 1/2 = 3.5
The side lengths of the triangles are determined by multiplying the corresponding lengths of ABC by their respective scale factors.