Question
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?
Answers
Steve
another of these triangle problems?
Have any ideas of your own on this one?
Have any ideas of your own on this one?
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.
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.
itrixie
I know the range is 14>x>4
itrixie
and the third side can not be 5 or 9
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
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?
13+12+11+10+9+8+7+6+5=81
14+13+12+11+10+8+7+6=81
Which one is it?
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
5+6+7+8+9+10+11+12+13 = 81
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.
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.
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
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