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In the figure above, DE and AC are parallel lines. If AC = 1
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20 Sep 2018, 16:57
20 Sep 2018, 16:57
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In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, and AD = 2, what is the length of AB?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
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Re: In the figure above, DE and AC are parallel lines. If AC = 1
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11 Apr 2020, 10:38
11 Apr 2020, 10:38
1
DE and AC are parallel lines, we have 2 pairs of equal angles
Let x = the length of BD and add in the other given lengths
At this point, we can see that there are two SIMILAR TRIANGLES within the diagram.
They are shown separately below.
KEY CONCEPT: The ratios of any two pairs of corresponding sides are always equal.
Sides DE and AC are corresponding, and sides BD and BA are corresponding
So, we can write: 8/12 = x/(x+2)
Cross multiply go get: (8)(x+2) = (12)(x)
Expand: 8x + 16 = 12x
We get: 16 = 4x
Solve: x = 4
Since side AB has length x + 2, we can conclude that the length of side AB = 4 + 2 = 6
Answer: E
Let x = the length of BD and add in the other given lengths
At this point, we can see that there are two SIMILAR TRIANGLES within the diagram.
They are shown separately below.
KEY CONCEPT: The ratios of any two pairs of corresponding sides are always equal.
Sides DE and AC are corresponding, and sides BD and BA are corresponding
So, we can write: 8/12 = x/(x+2)
Cross multiply go get: (8)(x+2) = (12)(x)
Expand: 8x + 16 = 12x
We get: 16 = 4x
Solve: x = 4
Since side AB has length x + 2, we can conclude that the length of side AB = 4 + 2 = 6
Answer: E
Re: In the figure above, DE and AC are parallel lines. If AC = 1
[#permalink]
11 Apr 2020, 10:39
11 Apr 2020, 10:39
Expert Reply
GREAT explanation Sir.
Regards
Regards
