Respuesta :

dashataran

Answer:

[tex]\text{DC = 6}[/tex]

Step-by-step explanation:

[tex]\text{Solution:}\\\text{Rectangle ABCD and rectangle A'B'C'D' are similar since the dimensions of }\\\text{rectangle ABCD are enlarged to form rectangle A'B'C'D'.}\\\\\therefore\ \dfrac{\text{A'B'}}{\text{AB}}=\dfrac{\text{C'B'}}{\text{CB}}\ \ \ [\text{Corresponding sides of similar rectangles are proportional.}]\\\\\text{or, }\dfrac{15}{\text{AB}}=\dfrac{9.5}{3.8}\\\\\text{or, AB}=\dfrac{15\times3.8}{9.5}=6[/tex]

[tex]\text{DC = AB = 6 [Opposite sides of rectangle are equal.]}[/tex]

Answer:

DC = 6 units

Step-by-step explanation:

the scale factor of the image A'B'C'D' from ABCD is calculated as

the ratio of corresponding sides , image to original , then

scale factor = [tex]\frac{B'C'}{BC}[/tex] = [tex]\frac{9.5}{3.8}[/tex] = 2.5

Then the original is image ÷ 2.5

Note that since the figures are rectangles, then D'C' = A'B' = 15, so

DC = 15 ÷ 2.5 = 6 units

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