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# geometry

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In triangle ABC, AB = AC = 25 and BC = 20. Points D, E and F are on sides AB, BC and AC respectively, such that DE and EF are parallel to AC  and AB respectively. What is the perimeter of parallelogram ADEF?

Jun 24, 2021

#2
+151
+2

knowing all that we can say that \$\overset{-}{DB}\$ and \$ \overset{-}{DE} \$ form an isosceles triangle so yes logically we get \$\overset{-}{AB}=\overset{-}{DE}+\overset{-}{FE}=25 \$

for the other side we can say that \$ \overset{-}{AF}  \$ and \$\overset{-}{DE}\$ have the same measurement -- so does \$\overset{-}{FE}\$ and \$\overset{-}{FC}\$ -- thus we can say that \$\overset{-}{AC} = \overset{-}{DE} +  \overset{-}{FE}  = 25\$

so yes, since we have the two sides just add them together

although may i know why i cannot edit the original answer?

Jun 24, 2021

#1
+151
+2

look at the image -- since \$ \overset{-}{AD} = \overset{-}{AC}   \$ then we can say that \$  \overset{-}{AB}=\overset{-}{DE}+\overset{-}{FE}=25    \$

its the exact same from the other point of view, so its P would be \$  25+25  \$, which is equal to 50

Jun 24, 2021
edited by UsernameTooShort  Jun 24, 2021
edited by UsernameTooShort  Jun 24, 2021
#2
+151
+2

knowing all that we can say that \$\overset{-}{DB}\$ and \$ \overset{-}{DE} \$ form an isosceles triangle so yes logically we get \$\overset{-}{AB}=\overset{-}{DE}+\overset{-}{FE}=25 \$

for the other side we can say that \$ \overset{-}{AF}  \$ and \$\overset{-}{DE}\$ have the same measurement -- so does \$\overset{-}{FE}\$ and \$\overset{-}{FC}\$ -- thus we can say that \$\overset{-}{AC} = \overset{-}{DE} +  \overset{-}{FE}  = 25\$

so yes, since we have the two sides just add them together

although may i know why i cannot edit the original answer?