Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an acute triangle.

a.4
b.5
c.6
d.11

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.

the least value out of the data shown is 5, maybe if you post a picture with it i could a little more.

step-by-step explanation:

the answer will be