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im totally confused about this question...
how would u do it?

One side of a triangel has length 6 and a second side has length 7. Which of the following could be the area of this triangle?

I. 13
II. 21
III.24

A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

i got B) II only but the answer is D) I and II only... i dont get how you would get an area of 13 since it's just going to be a line. help needed, thanks.

By Hairysam (Hairysam) on Thursday, April 08, 2004 - 01:49 am: Edit

bump!

By Aus10 (Aus10) on Thursday, April 08, 2004 - 01:51 am: Edit

You are correct in thinking that the minimum perimeter must be > 13 but the area can be a number much less than that if the angle between the two sides is really small. In theory the area could be < 1. The maximum possible area is 21 when the two sides form a right angle so the answer is D.

By Songster87 (Songster87) on Thursday, April 08, 2004 - 06:25 pm: Edit

Lines have a thickness of ZERO, not one.

If it was a line, you would have an area of zero.

Area just has to be greater than the "line" then.

Area cannot be greater than if the two formed right angles.

So, the area has to be GREATER than 0 and LESS THAN or EQUAL to 21. There are no other limitations.

By Gottagetout (Gottagetout) on Thursday, April 08, 2004 - 06:48 pm: Edit

If the triangle is allowed to be degenerate, then the area could be 0. Apparently the College Board doesn't believe in degenerate triangles, however. This cost me a perfect math score on the PSAT -- grrr.

By Aim78 (Aim78) on Thursday, April 08, 2004 - 06:55 pm: Edit

I asked this question several months back, and apparently it pops up frequently.

The answer is I and II. First think of a right triangle, because that is a triangle at its greatest area. One leg equals 6, the other equals 7. 1/2(6)(7) = 21, so you know the area could be 21. Now imagine the 90 degree angle in that right triangle reducing, reducing until it equals zero and the area equals zero. The area can be from 0 to 21, so the answer is I and II.