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If the length of side \(XZ\) is \(8,\) what is the area of triangle \(XYZ?\)

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If the length of side \(XZ\) is \(8,\) what is the area of triangle \(XYZ?\)

by M7MBA » Sat Jul 25, 2020 2:31 pm

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If the length of side \(XZ\) is \(8,\) what is the area of triangle \(XYZ?\)

(1) Angles \(XYZ\) and \(YZX\) measure \(60\) degrees.
(2) The shortest distance between point \(Y\) and line \(XZ\) is \(4\sqrt3.\)

[spoiler]OA=D[/spoiler]

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Re: If the length of side \(XZ\) is \(8,\) what is the area of triangle \(XYZ?\)

by sahilaro23 » Mon Jul 27, 2020 10:15 pm

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St1: Clearly means that it is an equilateral triangle. Hence sufficient.

St2: The shortest distance between point Y and line is 4rt3.
Shortest distance is possible with the point Y meet the XZ line at the mid point and that is possible only with the it is an equilateral. Using Pythagoras, we can find out either XY or YZ as 8. and hence the area can be calculate. Therefore, sufficient.

Answer, D.
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