Answer:
[tex]AB = 6[/tex]
Step-by-step explanation:
Given
[tex]BC = 3.8[/tex]
[tex]A'B' = 15[/tex]
[tex]B'C' = 9.5[/tex]
Required
Determine the length of AB
Because A'B'C'D is a dilation of ABCD, then the following relationship must exist:
[tex]A'B' : AB = B'C' : BC[/tex]
Substitute values for A'B', B'C' and BC
[tex]15 : AB = 9.5 : 3.8[/tex]
Express the ratio as fractions:
[tex]\frac{AB}{15} = \frac{3.8}{9.5}[/tex]
Multiply through by 14
[tex]15 * \frac{AB}{15} = \frac{3.8}{9.5} * 15[/tex]
[tex]AB = \frac{3.8}{9.5} * 15[/tex]
[tex]AB = \frac{3.8* 15}{9.5}[/tex]
[tex]AB = \frac{57}{9.5}[/tex]
[tex]AB = 6[/tex]
