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08 Dec 2014, 03:59
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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55% (01:48) correct
45%
(01:39)
wrong
based on 124
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What is the area of a plot of land which is in the shape of a quadrilateral?
(1) Only one angle, the one formed by the intersection of the two longest sides of the plot, measures 90 degree
(2) The sides of the quadrilateral measure 18m, 12m, 12m and 22m
(1) Only one angle, the one formed by the intersection of the two longest sides of the plot, measures 90 degree
(2) The sides of the quadrilateral measure 18m, 12m, 12m and 22m
08 Dec 2014, 06:58
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IMO E
1 => NOT SUFFICIENT. The sides are not mentioned.
2 => NOT SUFFICIENT. We can have multiple quadrilaterals
1 & 2 => NOT SUFFICIENT. We cannot form a quadrilateral combining 1 & 2. See the attachment. The hypotenuse of the triangle formed by the sides 18 and 22 is square root of 808 = 28.5. The remaining two sides are 12 & 12, so we cannot create a quadrilateral from the remaining sides. is my logic correct?
1 => NOT SUFFICIENT. The sides are not mentioned.
2 => NOT SUFFICIENT. We can have multiple quadrilaterals
1 & 2 => NOT SUFFICIENT. We cannot form a quadrilateral combining 1 & 2. See the attachment. The hypotenuse of the triangle formed by the sides 18 and 22 is square root of 808 = 28.5. The remaining two sides are 12 & 12, so we cannot create a quadrilateral from the remaining sides. is my logic correct?
Attachments
quadr.png [ 9.22 KiB | Viewed 5517 times ]
08 Dec 2014, 15:06
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Area of the quadrilateral = sum of the areas of 2 triangles.
(1) Not sufficient because there is no information about the lengths of the sides given.
(2) Not sufficient because there is no information about the angles given.
(1)+(2) Sufficient.
From the statement (1) we know that one angle is 90 degrees and that it is formed by the two longer sides, which are given in the statement (2) ( -->18 and 22). Hence, we know it's a right triangle. So we can find two important values from this: first, the area of this triangles will be (18*22)/2= 198; second, the hypotenuse of this triangle will be the base of the other triangle. By using the pythagorean theorem we can find the length of it. That will give us all the sides of the second triangle which will be isosceles triangles (12x12xhypotenuse of the first triangle). To find the area of this triangle we'll need height which will be equal to (12^2-(hypotenuse*1/2)^2) = height^2. After we'll know the height we can find the area of this triangle and add it to the area of the first triangle (198), which we already calculated.
(1) Not sufficient because there is no information about the lengths of the sides given.
(2) Not sufficient because there is no information about the angles given.
(1)+(2) Sufficient.
From the statement (1) we know that one angle is 90 degrees and that it is formed by the two longer sides, which are given in the statement (2) ( -->18 and 22). Hence, we know it's a right triangle. So we can find two important values from this: first, the area of this triangles will be (18*22)/2= 198; second, the hypotenuse of this triangle will be the base of the other triangle. By using the pythagorean theorem we can find the length of it. That will give us all the sides of the second triangle which will be isosceles triangles (12x12xhypotenuse of the first triangle). To find the area of this triangle we'll need height which will be equal to (12^2-(hypotenuse*1/2)^2) = height^2. After we'll know the height we can find the area of this triangle and add it to the area of the first triangle (198), which we already calculated.
