Properties Of Triangles

Let \(a, b, c\) be the lengths of sides of triangle \(A B C\) such that \(\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k\). Then \(\frac{(\mathrm{A}(\triangle \mathrm{ABC}))^2}{\mathrm{k}^4}=\)