An acute triangles two sides measure 8 and 15. How many possible lengths are there for the third side if it is an integer?

robotjeremyc Feb 9, 2019

#1**+1 **

Using the Triangle Inequality we have that

8 + 15 > x

23 > x

Also

8 + x > 15

x > 7

So.....the unknown side x can be

7 < x < 23

And there are 15 integers between 7 and 23

CPhill Feb 9, 2019

#2**+1 **

The answer is wrong because it has to be an acute triangle. Most of the 15 integers make the triangle an obtuse angle.

robotjeremyc
Feb 10, 2019

#3**+1 **

Thanks....I missed the "acute" part

The triangle will be obtuse if this is true

missing side > sqrt ( 15^2 + 8^2)

missing side > sqrt (289)

missing side > 17

And when x = 17...we have a right triangle

So.... the triangle will be acute when x = 8, 9, 10, 11, 12, 13, 14, 15, 16

So....9 values are possible for an acute triangle

CPhill
Feb 10, 2019