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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (01:42) correct
44%
(01:47)
wrong
based on 241
sessions
History
Date
Time
Result
Not Attempted Yet
If AD is 6, and ADC is a right angle, what is the area of triangular region ABC?
(1) Angle ABD = 60°
(2) AC = 12
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-ad-is-6-and-adc-is-a-right-angle-what-is-the-area-of-101200.html
23 Jul 2011, 03:14
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No matter what I do, I keep getting to "D" - can anyone help me out?
Info from the given:
Based on my understanding of ADC being right, the triangle MUST be isosceles, and triangles ABD and ADC are similar triangles. Is this correct??
Reasoning:
1) Knowing the given of the question, and we know that if angle ABD is 60 degrees => triangle is equilateral, and both triangles are similar triangles (both 30-60-90 triangles).
Knowing the "ratios" of a 30-60-90 triangle, and the dimensions of AD, we can find the value of ANY of the other sides, and hence the area. Sufficient
2) Knowing AD and AC, we can find DC by Pythagoras Theorem, and knowing triangles are similar, we can find the total area. Sufficient.
Can anyone lead me to "C", the OA? Or is the OA wrong?
Info from the given:
Based on my understanding of ADC being right, the triangle MUST be isosceles, and triangles ABD and ADC are similar triangles. Is this correct??
Reasoning:
1) Knowing the given of the question, and we know that if angle ABD is 60 degrees => triangle is equilateral, and both triangles are similar triangles (both 30-60-90 triangles).
Knowing the "ratios" of a 30-60-90 triangle, and the dimensions of AD, we can find the value of ANY of the other sides, and hence the area. Sufficient
2) Knowing AD and AC, we can find DC by Pythagoras Theorem, and knowing triangles are similar, we can find the total area. Sufficient.
Can anyone lead me to "C", the OA? Or is the OA wrong?
23 Jul 2011, 04:33
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MackyCee
Macky: If the triangle is right angled that does not mean that the triangle is isosceles. I could have been assumed as isosceles only if AD was also bisecting the angle A.
From statement 1 we can only find length of BD. Not sufficient
From statement 2 we can find only the length of DC. Hence not sufficient.
Combining both we get the height and the total base of the triangle, from which we can deduce the area.
