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

Question

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

anonymous · Answer

All three of them are possible as the triangle is not uniquely defined (because the length of the 3rd side is unknown)

anonymous · Answer

Answer booklet says D but that's the answer I originally had lol.

anonymous · Answer

is it right angled

anonymous · Answer

don't know, that's exactly how the question is worded. If it helps it's the last question on the sat math section, so I'm guessing it has some trick involved.

anonymous · Answer

no, i was mistaken, it is in fact only 13 and 21

anonymous · Answer

it is not right angled. The solution could be calculated using derivatives but it would be tedious because you have to express the area in terms of the 3 sides and then you would have to express the 3rd side in terms of x and then calculate the derivative of that function and then the maximum... instead, just check out this link: http://www.mathopenref.com/heronsformula.html you can just drag the 2 points to and make the 2 sides 6 and 7 and then experiment a little. You'll find that the area is 21 when the angle is a bit more than 90 degrees

anonymous · Answer

uh that's confusing lol but thanx