SOLUTION: Two sides of a triangle have sides 11 and 16. The length of the third side must be greater than _ and less than _. a. 5,27 b. 11,16 c. 4,28 d.10,17

Algebra ->  Triangles -> SOLUTION: Two sides of a triangle have sides 11 and 16. The length of the third side must be greater than _ and less than _. a. 5,27 b. 11,16 c. 4,28 d.10,17      Log On


   

Question 562160: Two sides of a triangle have sides 11 and 16. The length of the third side must be greater than _ and less than _.
a. 5,27 b. 11,16 c. 4,28 d.10,17
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
A, {5,27}.

One way to show this is to draw the longer side (16) first, then draw a circle with radius 11 centered at one of the longer side's endpoints. Any point on the circle can be the third vertex of the triangle, since the other two are fixed at 16 and 11. By taking "extreme" cases, you can see that the smallest and largest possible side lengths are 16-11 and 16+11 (5 and 27).