The ratio [tex]\frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F}[/tex] is also equal to 2:1
What are similar triangles?
"Two triangles are similar when their corresponding sides are in proportion to each other and corresponding angles are equal."
What is ratio?
"It is the comparison of two quantities of the same kind."
For given question,
ΔABC is similar to ΔDEF.
⇒ [tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex]
And ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
We know, if two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
⇒ [tex]\frac{area~of~\Delta {ABC}}{area~of~\Delta DE F} =(\frac{AB}{DE})^2 = (\frac{BC}{EF})^2 = (\frac{AC}{DF})^2[/tex]
We know, the perimeters of the similar triangles are in the same ratio as the sides.
[tex]\Rightarrow \frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F} = \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex]
The ratio of the length of AB to the length of DE is 2:1
[tex]\Rightarrow \frac{AB}{DE} = \frac{2}{1}[/tex]
[tex]\Rightarrow \frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F} = \frac{2}{1}[/tex]
Therefore, the ratio [tex]\frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F}[/tex] is also equal to 2:1
Learn more about similar triangles here:
https://brainly.com/question/25882965
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