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July 5, 2015

Posted by **Anonymous** on Tuesday, August 28, 2012 at 3:15pm.

The sides of a triangle are 5 cm, x cm, and y cm.

List possible values for x and y.

- geometry -
**Steve**, Tuesday, August 28, 2012 at 4:41pmsince any side is less than the sum of the other two sides,

x+y > 5 (duh)

x+5 > y

y+5 > x

lots of possible solutions:

5,11,9

5,13,13

and more

- geometry -
**Reiny**, Tuesday, August 28, 2012 at 5:02pmvalues of x could be 11, 12, or 13

values of y could be 9, 10, 11, 12 or 13

now overthinking the problem:

To have a triangle:

1. x+y > 5

2. x+5 > y ----> x-y > -5 or y-x < 5

3. y+5 > x ----> y-x > -5

from #2 and #2 we can see that

-5 < y-x < 5

so make 3 columns

5_x__y_(y-x)

5 11 9

5 11 10

5 11 11

5 11 12

5 11 13

5 12 9

5 12 10

..

5 12 13

5 13 9

..

5 13 13

in short, the x could be 11, 12 or 13

the y could be 9, 10, 11, 12, or 13

so the number of triangles for sides labeled x , y and 5 is 3(5) or 15

However, triangles 5 , 12, 13 and 5, 13, 12 are the same triangle

there are 3 such duplicated pairs, so

the actual number of triangles possible is 15-3 = 12