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555-605 (Medium)|   Geometry|               
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EMPOWERgmatRichC
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How come we can't find the answer with just statement one? We know the base of the triangle is 6 because QT = RS. So then why can't we create a line from angle P to QT to bisect the base, and then use pyth. theorem to find the height since we would have the hypotenuse (6) and the base (6/2). ?

Assuming only statement one, while we know the base QT of the triangle has length 6, there's no way we can determine the height without additional information. The reason the method that you suggested will not work is because we can draw the bisector of base QT from point P, but that won't meet QT in a right angle unless PQ = PT. We can also draw the perpendicular from point P onto the base QT, but that won't be the bisector unless again PQ = PT. Since we know PQ = QT, we could draw the perpendicular from point Q onto the base PT, which will also be the bisector of base PT; however, that won't help either because we don't know the length of PT.

One way of understanding why statement one alone is not sufficient is to notice that we only know the lengths of two sides of the triangle PQT, so that triangle could be one of the infinitely many triangles where two sides have lengths 6. Unless we know the measure of angle PQT or the length of side PT, we cannot determine the area of triangle PQT, which means we cannot answer the question.
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Video solution from Quant Reasoning:
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how do we come to the value 6 for the rectangle ?
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how do we come to the value 6 for the rectangle ?



The diagram shows that PQ = 6, and (1) says that PQ = RS, therefore, PQ = 6.

Hope it helps.
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