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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:44) correct
33%
(01:31)
wrong
based on 45
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In the figure given above, ABCD is a rectangle that is divided into five triangular regions. If triangles I, II and III have equal area and triangles IV and V have equal area, what is the area of rectangle ABCD?
(1) The area of triangle I is 30
(2) The area of triangle V is 15
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26 Dec 2022, 09:39
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File comment: Option D is the answer
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26 Dec 2022, 13:31
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Bunuel
The question stem provides us with a lot of "free" info, that we can use to our advantage and solve the question using observation and reasoning-
- The first thing that we observe is the perpendicular height of all the triangles is same (equals to length of side AD or side CB)
- Triangle I , II and III have the equal area, which means that the length of the base of triangle I, II and III is also equal.
- The base of triangle I and triangle II covers the entire length AB (therefore each base covers half the length of the rectangle), while the side DC comprises of the base of triangle II, V and IV. We already know that the length of the base of triangle I is same as the length of base triangle II, so triangle II covers half the length of DC and the other half (of the length) is shared by the triangle IV and triangle V.
- As the length of base of triangle IV and triangle V is half that of triangle II, the area of triangle IV and V is also half the area of triangle II.
As the dimensions of each triangle is related to the other, if we are given the area of any triangle we can find the area of the other triangles and thereby find the area of the rectangle ABCD.
Statements
(1) The area of triangle I is 30
(2) The area of triangle V is 15
Both statements individually provide us the area of one triangle. As we have already determined, knowing the area of any triangle is enough to determine the area of the rectangle ABCD, the statements are individually sufficient.
Option D
