# geometry

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?

1. 👍 0
2. 👎 0
3. 👁 83
1. another of these triangle problems?
Have any ideas of your own on this one?

1. 👍 0
2. 👎 0
posted by Steve
2. 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.

1. 👍 0
2. 👎 0
posted by Steve
3. I know the range is 14>x>4

1. 👍 0
2. 👎 0
posted by itrixie
4. and the third side can not be 5 or 9

1. 👍 0
2. 👎 0
posted by itrixie
5. 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

1. 👍 0
2. 👎 0
posted by itrixie
6. 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?

1. 👍 0
2. 👎 0
posted by itrixie
7. 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

1. 👍 0
2. 👎 0
posted by Steve
8. 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.

1. 👍 0
2. 👎 0
posted by Henry
9. 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

1. 👍 0
2. 👎 0
posted by Makayla

## Similar Questions

1. ### math

kaya brings her sister a stick to hold up a bird feeder. her sister says that she needs a stick that is 5/8 times as long as the stick kaya brought to her. kaya finds a stick that is longer than her first stick.

asked by autumn on June 1, 2015
2. ### Physics

On a sunny day, a 1.20 m long vertical stick in air casts a shadow 1.20 m long. If the same stick is held vertically and touching the flat bottom of a pool of salt water (n=1.71) half the height of the stick, how long is the

asked by SPENCER on January 8, 2012
3. ### physics

On a sunny day, a 1.20 m long vertical stick in air casts a shadow 1.20 m long. If the same stick is held vertically and touching the flat bottom of a pool of salt water (n=1.71) half the height of the stick, how long is the

asked by alex giroux on January 8, 2012
4. ### physics

A uniform 2.00-m-long stick is raised at an angle of 30° to the horizontal above a sheet of ice. The bottom end of the stick rests on the ice. The stick is released from rest. The bottom end of the stick remains in contact with

asked by Sandhya on April 1, 2010
5. ### Math-percents

A carpenter has a wooden stick that is 84cm long.she cuts off 25% from the end of the stick .then she cuts the remaining stick into 6 equal pieces.what is the length of each piece?

asked by Nyelle smith on January 5, 2015
6. ### Math

A carpenter has a wodden stick that s 84 centimeters long.She cuts of 25% from the end of the stick.Then she cuts the remaining stick into 6 equal pieces.What is the lenght of each piece?

asked by Armani on November 29, 2014
7. ### Math

A carpenter has a wooden stick that is 84 centimeters long. She cuts off 25% from the end of the stick. Then she cuts the remaining stick into 6 equal pieces. What is the length of each piece?

asked by Alli on December 5, 2012
8. ### physics

A uniform stick 1.5 m long with a total mass of 210 g is pivoted at its center. A 3.9-{\rm g} bullet is shot through the stick midway between the pivot and one end The bullet approaches at 250 {\rm{ m}}/{\rm{s}} and leaves at 140

asked by Anonymous on April 26, 2011
9. ### Physics

At 08:00hrs a 2.7- m-long vertical stick in air casts a shadow 1.8 m long. If the same stick is placed at 08:00hrs in air in a flat bottomed pool of salt water half the height of the stick, how long is the shadow on the floor of

asked by Katie on May 27, 2008
10. ### Physics

At 10:00hrs a 1.5- m-long vertical stick in air casts a shadow 1.4 m long. If the same stick is placed at 10:00hrs in air in a flat bottomed pool of salt water half the height of the stick, how long is the shadow on the floor of

asked by Lindsay on May 27, 2008

More Similar Questions