bryan88 wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?
Dear
bryan88
I see the GMAT guru posted a link, but I'll show a solution here. See my diagram below.
Imagine the side with length 12 (AB) is horizontal, and we are swinging the angle of the side with length 8 (AC) --- in the diagram, the three different C's show three different possible positions.
Of course, area = (1/2)b*h. The base of all these possible triangles is 12. When AC is perpendicular (shown as C2 in the diagram), then h = 8; otherwise, h is something less than 8.
This means the triangle with maximum area occurs when the 8 & 12 are perpendicular --- that triangle has an area of A = (1/2)b*h = (0.5)(8)(12) = 48.
Since h can be anything between 0 and 8, the area can be any value between 0 and 48. Thus, 35 is allowed as a possible value, and 48 of course is allowed --- it's the maximum possible value. The area of 56 is not possible.
Thus, answer =
B
Does that make sense? Let me know if you have any further questions.
Mike
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