In the figure above, if AB is parallel to DE, DC = EC, what is the per

In the figure above, if AB is parallel to DE, DC = EC, what is the perimeter of triangle DEC?


(1) BE is 5/7 of BC

(2) AC = 13 and AB = 7

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Attachment:

image014.jpg

Solution

Step 1: Analyse Question Stem

• Look at the diagram given,

o If \(DE\) is parallel to \(AB\), then triangle \(ABC\) is similar to triangle \(DEC\).

 Thus, \(\frac{EC}{BC} = \frac{DC}{AC}=\frac{DE}{AB}\)
• Now, by using this property let’s solve the given problem.

o \(AB\) is parallel to \(DE\)

 Triangle \(ABC\) is similar to triangle \(DEC\).
• Thus, \(\frac{EC}{BC}=\frac{DC}{AC}=\frac{DE}{AB}\)

 It is also given that \(DC = EC.\)
 \(DE = 2\) units

• \(DE+EC+DC = 2 + EC + DC= 2+2DC\) [it is given that \(DC = EC\)]

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• \(\frac{BE}{BC} = \frac{5}{7}\)

o \(1-\frac{BE}{BC} = 1 – \frac{5}{7}\) [Subtracting both the sides from \(1\)]
o \(\frac{(BC-BE)}{BC} = \frac{2}{7} \)
o EC/BC = 2/7, [BE+EC = BC]
• It means \(\frac{EC}{BC} = \frac{DC}{AC}=\frac{DE}{AB} = \frac{2}{7}\).
• With this information we can find the ratio of sides, but we cannot find the value of \(DC\) or \(EC\).

• \(\frac{DC}{AC} = \frac{DE}{AB}\)

o \(\frac{DC}{13} = \frac{2}{7}\)
o \(DC = \frac{26}{7}\)
• Perimeter of triangle DEC = \(2 + 2*\frac{26}{7}\)