Answer:
11
Step-by-step explanation:
First of all, for what values of x can we have a triangle.
By triangle inequality, we have that 10-5<x<10+5.
Simplifying this gives us 5<x<15.
So the answer is either 6 or 11.
An acute triangle with sides where is the largest then .
Now if the triangle is acute (with the assumption x is the largest) then:
This implies that with the condition that x>10 since we assumed it largest so the actual restriction on x is:
()
So this includes 11 and not 6.
Now if the triangle is acute (with the assumption x is not the largest) then:
This means that with condition x is less than 10 since we are assuming x is not the largest.
()
So this mean that x would have to be included between and 10.
Either way 6 is not included in either of the acute triangle cases.
11 is the only one that satisfies the condition in at least one of the cases.
is true and 11 is a number between 5 and 15.