Discussion
What is the area of the triangle above?
(1) a = x, b = 2x, and c = 3x.
(2) The side opposite a is 4 and the side opposite b is 3.
| (A) | if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient; |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 03/05/2012 06:10
Takig 1 and 1 together we get contrdiction: a=30' and line opposit a is 8 which means that hipotinuis is 8 (because sin30=.5)
but from pithagorous rule hipotinuis is 5 -> so it is impossible that a is 30and the side opposit it is 4 and another is 3, so there ia a contradiction between 1 and 2 , how can we use them together in order ti get the answer????!!!!!
but from pithagorous rule hipotinuis is 5 -> so it is impossible that a is 30and the side opposit it is 4 and another is 3, so there ia a contradiction between 1 and 2 , how can we use them together in order ti get the answer????!!!!!
Posted: 03/06/2012 12:17
Vvv, statement 2 explicitly says the side opposite a is 4, not 8.
Posted: 03/06/2012 12:15
Vvvv, from (1), we only know that a = 30 degrees, b=60,, and c=90 (even though the picture is not drawn proportionally). But this is not enough to calculate the triangle.
From (2), we know that the side opposite a, which is the base, is 4, and the side opposite b, which is the height, is 3. But we can't calculate the area using (2) only, because we don't know the value of any of the angles.
Once we combine the two statements, we know that c is a right angle, so the area can be easily calculated as 1/2 * 3 * 4. So in this case, both statements are required to answer the question.
From (2), we know that the side opposite a, which is the base, is 4, and the side opposite b, which is the height, is 3. But we can't calculate the area using (2) only, because we don't know the value of any of the angles.
Once we combine the two statements, we know that c is a right angle, so the area can be easily calculated as 1/2 * 3 * 4. So in this case, both statements are required to answer the question.