The shorter sides of an acute triangle are x cm and 2x cm. the longest side of the triangle is 15 cm. what is the smallest possible whole-number value of x

For an acute angled triangle 

h^2 < x^2 + y^2      where h = longest side and x and y are the other 2 sides.

so here we have

15^2 <  x^2 + (2x)^2

15^2 <  5x^2

x^2 >  15*3 = 45
x > sqrt 45 or x > 6.7

So smallest whole number value of  x is 7