Question

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

Answer 1

First x must satisfy
10-5 < x < 5+10
5 < x < 15
To have a triangle

Answer 2

Now you need an acute triangle, so how do you proceed?

Answer 3

If you take x near 5, then the angel opposite to 10 will be obtus

Answer 4

If you take x such that
x^2 = 5^2 + 10^2=125, then the angle opposite to x will be 90 degrees

Answer 5

sqrt(125)=11.1803,
try take x =11 and show that your triangle will be acute

Answer 6

Did you understand?

Answer 7

Yes, I'm beginning to understand now. Thanks for the help!