I have to get this math problem right to receive an A in the class. The problem was something like a circle inscribed in a hexagon. The answer was 2:3. I got 3:2. I must come up with an argument that it didn't matter so I can get the problem correct! It might be impossible, but I'm sure my teacher can be convinced by a bit of wordplay haha.
-
It all depends on how the problem is worded, but unfortunately, your teacher's right. A ratio must have two things to be considered "correct"...it must specify which item comes first (ie the ratio of A to B, versus the ratio of B to A), and it must have the numbers in the right order.
If the problem is worded "What is the ratio of the area of the hexagon to the area of the circle", then you're screwed. 3:2 says the hexagon's 1.5 times bigger than the circle. 2:3 says the hexagon's 2/3 the size of the circle...in other words, that the hexagon is smaller.
If your teacher GAVE you the diagram, you could state that it's obvious which one's bigger. But still, you gave it in the wrong order.
If the problem says "Give the ratio of the areas", but doesn't specify which is to come first, then your answer of simply 3:2 is incomplete, but slightly more forgivable. It's kind of like saying "How far did he go?", and you say "20." The problem is...20 of WHAT? In your example, it's 3:2, but which is first? Again, if there's a picture, it should be obvious which is first.
There is, however, exactly one type of ratio where order doesn't matter. Unfortunately it's a rather trivial ratio...1:1, or 2:2, or x:x. In that case, they're the same size. If you say the ratio of the areas is 1:1, it doesn't matter which one you put first and which one you put second...they're both the same size either way!
IMO, you probably should get something off. After all, you gave the ratio in the wrong order. However, assuming that there was some other type of work involved (ie you had to draw auxillary radii to the sides of the hexagon, and then you had to notice that the radius to the side of the hexagon was perpendicular to the side, etc.), then you should get partial credit...particularly if you're in a high school geometry class and the point of the lesson was the geometry of the situation, and not computing ratios. If you're in pre-algebra (which I doubt), and you're JUST learning ratios...well, this may be the point of the question.
If the problem is worded "What is the ratio of the area of the hexagon to the area of the circle", then you're screwed. 3:2 says the hexagon's 1.5 times bigger than the circle. 2:3 says the hexagon's 2/3 the size of the circle...in other words, that the hexagon is smaller.
If your teacher GAVE you the diagram, you could state that it's obvious which one's bigger. But still, you gave it in the wrong order.
If the problem says "Give the ratio of the areas", but doesn't specify which is to come first, then your answer of simply 3:2 is incomplete, but slightly more forgivable. It's kind of like saying "How far did he go?", and you say "20." The problem is...20 of WHAT? In your example, it's 3:2, but which is first? Again, if there's a picture, it should be obvious which is first.
There is, however, exactly one type of ratio where order doesn't matter. Unfortunately it's a rather trivial ratio...1:1, or 2:2, or x:x. In that case, they're the same size. If you say the ratio of the areas is 1:1, it doesn't matter which one you put first and which one you put second...they're both the same size either way!
IMO, you probably should get something off. After all, you gave the ratio in the wrong order. However, assuming that there was some other type of work involved (ie you had to draw auxillary radii to the sides of the hexagon, and then you had to notice that the radius to the side of the hexagon was perpendicular to the side, etc.), then you should get partial credit...particularly if you're in a high school geometry class and the point of the lesson was the geometry of the situation, and not computing ratios. If you're in pre-algebra (which I doubt), and you're JUST learning ratios...well, this may be the point of the question.
-
With such a limited amount of information and bad intentions, I'm afraid neither me nor anyone else will be able to help you.
It seems as though you simply don't deserve an A grade.
It seems as though you simply don't deserve an A grade.