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In the figure above, line m is parallel to the x-axis. If I, II and II

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In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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In the figure above, line m is parallel to the x-axis. If I, II and III designate the respective areas of the triangles shown, which of the following is true?

(A) I > II > III
(B) II > III > I
(C) III > I > II
(D) I = III > II
(E) I = II = III


[Reveal] Spoiler:
Attachment:
2017-09-01_1133_001.png
2017-09-01_1133_001.png [ 10.82 KiB | Viewed 545 times ]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Sep 2017, 11:18, edited 1 time in total.
Edited the OA.

Kudos [?]: 128710 [0], given: 12182

Director
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Joined: 22 May 2016
Posts: 806

Kudos [?]: 258 [0], given: 546

Re: In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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New post 01 Sep 2017, 09:15
Bunuel wrote:
Image
In the figure above, line m is parallel to the x-axis. If I, II and III designate the respective areas of the triangles shown, which of the following is true?

(A) I > II > III
(B) II > III > I
(C) III > I > II
(D) I = III > II
(E) I = II = III


[Reveal] Spoiler:
Attachment:
2017-09-01_1133_001.png

Triangles have equal height

The vertices of each triangle used to determine height (with bases that lie on x), lie on line m.

Drop a perpendicular altitude from top vertex to base on x-axis, for each triangle.

Altitudes are equal: 1) all lengths of perpendicular lines between two parallel lines are equal; 2) all y-coordinates are equal; 3) all altitudes are perpendicular to bases that lie on the same straight line (x-axis).

Heights can be designated as (m - 0) = m, because both vertices of the base of all three triangles lie on the x-axis where y equals 0.

Bases are equal

The base of all three triangles is equal. Subtract the x-coordinates.
(2 - 1) = 1
(4 - 3) = 1
(7 - 6) = 1

Area of all three triangles (I, II, and III), therefore, is \(\frac{(1 * m)}{2}\) = \(\frac{m}{2}\)

I = II = III

Answer E

Kudos [?]: 258 [0], given: 546

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Re: In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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New post 12 Sep 2017, 12:40
The correct answer is option E. As all the triangles have same height (between m and x) and same base (1 unit), so the area is also same.

Bunuel : please change the OA after review.

Kudos [?]: 12 [0], given: 88

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Re: In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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New post 22 Sep 2017, 09:30
The answer is still D.

Kudos [?]: 7 [0], given: 24

Re: In the figure above, line m is parallel to the x-axis. If I, II and II   [#permalink] 22 Sep 2017, 09:30
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In the figure above, line m is parallel to the x-axis. If I, II and II

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