Longest Side of Triangle

harpazo

harpazo

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The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 45?

Solution:

The consecutive integers are x, x + 2 and x + 4. I do not understand why x + 2 and x + 4, both of which include an even number is the proper set up. Can someone explain the logic behind using even numbers to find odd consecutive integers.

x + x + 2 + x + 4 = 45

3x + 6 = 45

3x = 45 - 6

3x = 39

x = 39/3

x = 13

Answer: The length of the longest side of the triangle is 17.
 
Let x be the first number, which is assumed to be odd. The next odd number is found by adding 2 (e.g. 13 + 2 = 15, 15 + 2 = 17). So the second number is x+2, and the third is found by adding 2 again, to get x+2+2 = x+4.

Yes, a lot of students are initially confused by that, but after you've seen it once, it should no longer be a surprise. The many students I've seen who write things like x, x+1, x+3 on a unit test clearly have never taken the time to think through it slowly, and are just doing what feels right. (I'm not saying this is you, just that it is awfully common, and reflects a misunderstanding of what it means to learn math.)

So I suggest that you avoid just treating "x, x+2, x+4" as a magic formula that came down from the sky, and take it slowly for every problem you do: If the first number is x, how do I get the next number from it?

By the way, if you wanted, since they ask only for the longest side, you could define that as x, so the three sides would be x-4, x-2, x, and when you solved the equation you would immediately get what they are asking for. (I don't recommend this, because it would be easy to make a mistake, and you want to find all three anyway to check. But it would force you to do more thinking, which might be good!
 
Dr.Peterson said:
Let x be the first number, which is assumed to be odd. The next odd number is found by adding 2 (e.g. 13 + 2 = 15, 15 + 2 = 17). So the second number is x+2, and the third is found by adding 2 again, to get x+2+2 = x+4.

Yes, a lot of students are initially confused by that, but after you've seen it once, it should no longer be a surprise. The many students I've seen who write things like x, x+1, x+3 on a unit test clearly have never taken the time to think through it slowly, and are just doing what feels right. (I'm not saying this is you, just that it is awfully common, and reflects a misunderstanding of what it means to learn math.)

So I suggest that you avoid just treating "x, x+2, x+4" as a magic formula that came down from the sky, and take it slowly for every problem you do: If the first number is x, how do I get the next number from it?

By the way, if you wanted, since they ask only for the longest side, you could define that as x, so the three sides would be x-4, x-2, x, and when you solved the equation you would immediately get what they are asking for. (I don't recommend this, because it would be easy to make a mistake, and you want to find all three anyway to check. But it would force you to do more thinking, which might be good!
Click to expand...

The thinking part of application, you know, thinking that leads to forming an equation is my number one goal.
 
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