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Difficulty:
15%
(low)
Question Stats:
83% (01:18) correct
17%
(01:31)
wrong
based on 48
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ABCD is a parallelogram, and AED is an equilateral triangle. If C is the midpoint of DE, and the perimeter of ∆AED is 12, what is the perimeter of ABCD?
(A) 16
(B) 14
(C) 12
(D) 10
(E) 9
Attachment:
2017-11-12_2103_001.png [ 6.06 KiB | Viewed 4079 times ]
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Solution:
- It is given that \(\triangle AED\) is an equilateral triangle with a perimeter of 12
- This means side \(AE=ED=DA=\frac{12}{3}=4\)
- \(C\) is the midpoint \(ED\) which means \(EC=CD=\frac{4}{2}=2\)
- It is given that \(ABCD\) is a parallelogram
- This means side \(AD=BC=4\) and \(AB=CD=2\) because opposite sides of a parallelogram are equal
Attachment:
triparra.png [ 27.06 KiB | Viewed 1133 times ]
- Perimeter of parallelogram \(ABCD=2+4+2+4=12\)
Hence the right answer is Option C
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