(Solved): Please use JAVA Computing the Perimeter and the Area of a Triangle Given Its Side Lengths: Examine t ...

Computing the Perimeter and the Area of a Triangle Given Its Side Lengths: Examine the formulas given on the right side for the illustrated triangle with side lengths $\mathbf{a},\mathbf{b}$ and $\mathbf{c}$. - The triangle inequality theorem states that each side of a triangle must be shorter than the other two sides added together. - The perimeter of a triangle can be computed as the sum of its side lengths. - The area of a triangle can be computed by using Heron's formula given its side lengths. Write a program that - reads the lengths of the 3 sides of a triangle $(\mathbf{a},\mathbf{b}$ and $\mathbf{c})$ from the user, - checks if the user-entered values form a valid triangle by using the triangle inequality theorem, - prints "Invalid input." if the user-entered values do not form a valid triangle, - and computes then prints the perimeter and the area of the triangle otherwise (i.e., when the user-entered values form a valid triangle). Heron's Formula: $\begin{array}{l}\text{ area }=\sqrt{s(s?a)(s?b)(s?c)}\\ \text{ where }s=\frac{\text{ perimeter }}{2}\end{array}$