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E
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Difficulty:
15%
(low)
Question Stats:
82% (00:44) correct
18%
(01:20)
wrong
based on 87
sessions
History
Date
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Not Attempted Yet
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 2524 times ]
01 Sep 2017, 09:15
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Bunuel
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
chipsy
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12 Sep 2017, 12:40
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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.
Bunuel : please change the OA after review.
