answer my 7th grade math question?

Question

please help


the perimeter of any triangel is the sum of the lengths of its sides.the lengths of the sides of a certain triangle,in feet, are consecutive even numbers. the perimeter of this triangle is between 10 feet to 24 feet inclusive.list all possible lengths for the longest side of the triangle.

Answer 1

2-4-6
4-6-8
6,8,10
6, 8, and 10 are longest sides

Answer 2

Because the numbers are small, you can try all possibilities:

2+4+6 = 12 (good, except this is a "flat" triangle)
4+6+8 = 18 (good)
6+8+10 = 24 (good)
8+10+12 = 30 (too big)

Regarding the 2+4+6 triangle:
I suspect that in 7th grade, a flat triangle could be considered not a triangle. The two small sides are exactly on the long side: there is no inside. This triangle has no height. It has a surface of exactly zero. It looks like a line segment of length 6.

However, in maths, this is still considered a triangle. Some refer to it as a degenerate triangle.

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If the problem had been with much bigger numbers (or with more complicated conditions) you would have used an equation:

The three sides are consecutive even numbers:

x, x+2 and x+4

perimeter = x + x+2 + x+4 = 3x + 6

The perimeter cannot be less than 10:

3x + 6 >= 10
>= means greater than or equal to
3x >= 4
x >= 4/3 = 1+ 1/3
therefore, x has to be at least 2 (the first even number above 4/3)

The perimeter cannot be more than 24

3x + 6 <= 24
(less than or equal)
3x <= 18
x <= 6
x cannot be greater than 6

Because x must be even, these conditions only allow us to use
x=2 (triangle = 2+4+6),
x=4 (triangle = 4+6+8) and
x=6 (triangle = 6+8+10)
which is what we got above.

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Message for Joe Capo:

The Pythagorean theorem works for triangles that have a right angle (an angle of 90 degrees).
The only case with three consecutive even numbers is:
6, 8, 10.
6 squared = 36,
8 squared = 64 and
10 squared = 100 = 36+64

So the Pythagorean theorem tells us that the biggest possible triangle that meets the conditions of the problem, is a right-angle triangle.
http://en.wikipedia.org/wiki/Pythagorean_theorem
(this will bring back memories)

Answer 3

Oh wow, I haven't done probability in a while. Hmm... first, figure out the total number of possible combinations from the set. So that's 5+4+3+2+1 (because 6 has 5 possible pairings, then 5 already had 5*6 taken up, so it only has 4 possible pairings, etc... if this doesn't make sense, draw a picture. Just do 2 columns of numbers (6, 5, 4, 3, 2, and 1), then connect numbers on the left to possible pairings on the right, and count the lines as you draw them. Don't do right to left, though, since 4*5 is the same thing as 5*4. You also don't have to do 6*6, 5*5, etc, since the question says DIFFERENT numbers) Then find the number of combinations that multiply to 12 - 6*2 and 3*4 (I hope I didn't miss any?), which is 2 combos out of a total 15 So, the probability is 2/15.

Answer 4

Take the consecutive even numbers as (2n-2) 2n and (2n+2).So the perimeter is 6n where n is a integer

6n=24 and the longest side = 10 feet
6n=18 " =8 feet
6n=12 " = 6feet There are NO other .

Answer 5

Longest sides are 6, 8 and 10

Answer 6

6, 8, and 10

Answer 7

x + x+2 + x+4 = 18
3x =12

x = 4 Longest side is x+4 = 8

Answer 8

USe the pathegriam theroem or however you spell it, I've been outa school for 3 years so go easy on me :)

Answer 9

Teachers have a email to you know.Also one of those guys has to be wrong.[My uncle is a teacher and does have a email]

Sincerly,Flave