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Updated on: 28 Sep 2012, 07:31
Originally posted by ankurjohar on 28 Sep 2012, 07:25.
Last edited by Bunuel on 28 Sep 2012, 07:31, edited 1 time in total.
Last edited by Bunuel on 28 Sep 2012, 07:31, edited 1 time in total.
Edited the question.
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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)!
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PQST.png
If PQ is 6 and QS is 8 in rectangle PQST, what is the height of the triangle QRS?A. 1
B. 2
C. 3
D. 3√3
E. This cannot be determined from the information above.
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28 Sep 2012, 10:25
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ankurjohar
Usually it is mentioned that "drawing not scaled", meaning we shouldn't draw any conclusion based on "what it looks like".
Here, it looks like triangle QRS is isosceles and we are asked to find the height corresponding to the base QS.
Only in an equilateral triangle are all heights equal. If QRS is not isosceles, and lacking any additional information, we cannot find any of its heights.
So, if QRS is isosceles and if it is meant the height corresponding to the base QS, here is a way to find it (refer to the attached drawing):
QT = PS = 10, diagonals of the rectangle (6, 8, 10 triplet).
Radius of the circle is therefore 5, so OR = OS = 5.
QRSO is a kite (QR = RS assumption, QO = OS radii). In a kite, the diagonals are perpendicular.
Then, RO is parallel to QP being both perpendicular to QS.
It follows that VO is half of QP, so VO = 6/2 = 3 (VO is midline in triangle SQP).
Then, the height RV = RO - VO = 5 - 3 = 2.
Answer B.
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RectangleInCircle.jpg [ 29.91 KiB | Viewed 2523 times ]
28 Sep 2012, 10:56
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Triangles don't have one "height"; they have three different heights depending which base you choose. And even if we assume they want us to take QS as the base, the answer is still E unless you are told the triangle is isosceles. So the question is deeply flawed.
Anyway, assuming QS is our base, and that QR = RS, then the length of a diagonal of our rectangle is equal to the diameter of the circle. So the diameter is 10. Draw the line OR, where O is the circle's center. That's a radius, so its length is 5. If OR intersects the rectangle at the point A, then OA is half the width of the rectangle, so is 3, and the length of AR, which we want to find, is thus 5 - 3 = 2.
Anyway, assuming QS is our base, and that QR = RS, then the length of a diagonal of our rectangle is equal to the diameter of the circle. So the diameter is 10. Draw the line OR, where O is the circle's center. That's a radius, so its length is 5. If OR intersects the rectangle at the point A, then OA is half the width of the rectangle, so is 3, and the length of AR, which we want to find, is thus 5 - 3 = 2.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
