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05 Aug 2021, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
79% (01:21) correct
21%
(01:55)
wrong
based on 86
sessions
History
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Time
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Lines m and n are parallel. If the length of AB is 12, what is the perpendicular distance between m and n ?
A. \(4\sqrt{3}\)
B. 6
C. \(6\sqrt{2}\)
D. \(6\sqrt{3}\)
E. 12
Attachment:
1.png [ 9.03 KiB | Viewed 1850 times ]
05 Aug 2021, 02:39
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Solution:
Let us drop a perpendicular from point \(A\) to line \(n\) at point \(C\).
Thus, we can say that we need the value of \(AC\).
We have a right angle triangle \(ABC\) right angles at \(C\).
Exterior angle \(\angle B = 150^o\) (Corresponding angle because line \(m||n\)). And interior angle \(\angle B = 180-150=30^o \)
Thus, \(\triangle ABC\) becomes a \(30^o-60^o-90^o\) triangle.
parallel1.png [ 13.01 KiB | Viewed 1704 times ]
We know in a \(30^o-60^o-90^o\) triangle, sides are in ratio \(1:\sqrt3:2\)
Let the sides be \(AC=x, BC=\sqrt3 x\) and \(BA=2x\).
We know \(BA=2x=12\) or \(x=6\).
Thus side \(AC=x=6\).
Alternate solution if you know trigonometry:
In \(\triangle ABC\), we can say \(Sin 30=\frac{AC}{BA} \)
\(⇒ \frac{1}{2}=\frac{AC}{12}\)
\(⇒ AC=\frac{12}{2}=6\)
Hence the right answer is Option B.
Let us drop a perpendicular from point \(A\) to line \(n\) at point \(C\).
Thus, we can say that we need the value of \(AC\).
We have a right angle triangle \(ABC\) right angles at \(C\).
Exterior angle \(\angle B = 150^o\) (Corresponding angle because line \(m||n\)). And interior angle \(\angle B = 180-150=30^o \)
Thus, \(\triangle ABC\) becomes a \(30^o-60^o-90^o\) triangle.
Attachment:
parallel1.png [ 13.01 KiB | Viewed 1704 times ]
We know in a \(30^o-60^o-90^o\) triangle, sides are in ratio \(1:\sqrt3:2\)
Let the sides be \(AC=x, BC=\sqrt3 x\) and \(BA=2x\).
We know \(BA=2x=12\) or \(x=6\).
Thus side \(AC=x=6\).
Alternate solution if you know trigonometry:
In \(\triangle ABC\), we can say \(Sin 30=\frac{AC}{BA} \)
\(⇒ \frac{1}{2}=\frac{AC}{12}\)
\(⇒ AC=\frac{12}{2}=6\)
Hence the right answer is Option B.
