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02 Aug 2021, 17:11
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
89% (01:38) correct
11%
(02:44)
wrong
based on 38
sessions
History
Date
Time
Result
Not Attempted Yet
In the accompanying diagram, ABCD is an isosceles trapezoid with AB||DC. If AB = 8, DC = 16, and altitude AE = 3, what is the perimeter of trapezoid ABCD?
1.png [ 24.39 KiB | Viewed 1732 times ]
A. 29
B. 34
C. 40
D. 42
E. 44
Attachment:
1.png [ 24.39 KiB | Viewed 1732 times ]
B. 34
C. 40
D. 42
E. 44
02 Aug 2021, 17:14
Kudos
Bookmarks
OE
To find the perimeter of trapezoid ABCD we need to know the length of AD.
Since AD is also a side in right triangle ADE, \((AD)^2 = (AE)^2 + (DE)^2. \)
Draw an altitude from B intersecting at F.
3.png [ 28.19 KiB | Viewed 1692 times ]
Because the trapezoid is isosceles, DE = FC,
and EF = 8 and DE + EF + FC = 16, the length of is 4,
thus,\((AD)^2 = 32 + 42\)
=> AD = 5.
Since the legs of an isosceles trapezoid are congruent,
the perimeter of ABCD = 5 + 8 + 5 + 16 = 34
IMO answer is B
To find the perimeter of trapezoid ABCD we need to know the length of AD.
Since AD is also a side in right triangle ADE, \((AD)^2 = (AE)^2 + (DE)^2. \)
Draw an altitude from B intersecting at F.
Attachment:
3.png [ 28.19 KiB | Viewed 1692 times ]
Because the trapezoid is isosceles, DE = FC,
and EF = 8 and DE + EF + FC = 16, the length of is 4,
thus,\((AD)^2 = 32 + 42\)
=> AD = 5.
Since the legs of an isosceles trapezoid are congruent,
the perimeter of ABCD = 5 + 8 + 5 + 16 = 34
IMO answer is B
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