Asked by itrixie

A stick 5 cm long, a stick 9 cm long, and a third stick n cm long form a triangle. What is the sum of all possible whole number values of n?
Answered by Steve
another of these triangle problems?
Have any ideas of your own on this one?
Answered by Steve
as a hint, suppose you joined the two sticks at the end.

Now consider rotating the smaller one, from being end-to-end with the larger one, to overlapping it. What's the max and min possible length for the third side?

Now list all the integers in that range and add 'em up.
Answered by itrixie
I know the range is 14>x>4
Answered by itrixie
and the third side can not be 5 or 9
Answered by itrixie
so that leaves 6, 7, 8, 10, 11, 12,and 13. That added up all together is 67 but my teacher said that was incorrect
Answered by itrixie
14+13+12+11+10+9+8+7+6+5+4=99
13+12+11+10+9+8+7+6+5=81
14+13+12+11+10+8+7+6=81
Which one is it?
Answered by Steve
Of course the 3rd side can be 5 or 9. That just makes an isosceles triangle. So, you want all the numbers n such that 4 < n < 14:
5+6+7+8+9+10+11+12+13 = 81
Answered by Henry
9<n<14
Values of n: 10, 11, 12, 13.
Sum = 10+11+12+13 = 46 cm.

5<n<9
Values of n: 6, 7, 8.
Sum = 6+7+8 = 21 cm.

n = 5 cm(Isosceles Triangle).

n = 9 cm(Isosceles Triangle).

Sum Total=5+6+7+8+9+10+11+12+13 = 81 cm.



Answered by Makayla
I say use the Pythagorean theorem.
a^2+b^2=C^2.
5^2+9^2=C^2
25+81=106
THEN DO THE SQUARE ROOT OF 106 WHICH IS 10.30CM
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