Answer: The smallest <span>possible whole-number value of x</span> is 7
Explanation: Assume sides of the triangle are: a = x b = 2x c = 15 We are given that c is the longest side For the triangle to be acute: c^2 < a^2 + b^2
Substitute with the values of a, b and c and solve for x as follows: c^2 < a^2 + b^2 (15)^2 < (x)^2 + (2x)^2 225 < x^2 + 4x^2 225 < 5x^2 45 < x^2
For we will get the zeros, this means that we will solve for x^2 = 45: x^2 = 45 x = + or - √45 This means that: either x = 6.708 oR x = -6.708
We want the x^2 to be greater than 45. This means that we want the x to be greater than 6.708 Therefore, the smallest possible whole number to satisfy this condition is 7.