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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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Math Expert
Joined: 02 Sep 2009
Posts: 47064
In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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Updated on: 22 Sep 2017, 11:18
00:00

Difficulty:

35% (medium)

Question Stats:

81% (00:29) correct 19% (00:35) wrong based on 64 sessions

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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

Attachment:

2017-09-01_1133_001.png [ 10.82 KiB | Viewed 876 times ]

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Originally posted by Bunuel on 01 Sep 2017, 00:41.
Last edited by Bunuel on 22 Sep 2017, 11:18, edited 1 time in total.
Edited the OA.
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Joined: 22 May 2016
Posts: 1827
Re: In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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01 Sep 2017, 09:15
Bunuel wrote:

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

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

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Joined: 05 Oct 2014
Posts: 23
Concentration: Finance, Entrepreneurship
Re: In the figure above, line m is parallel to the x-axis. If I, II and II [#permalink]

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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.
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Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
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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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22 Sep 2017, 09:30
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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