Let \(b\) be the base and \(a\) be the altitude of the triangle.

\(b = a- 4 \)

\(A_t = 126\)

\(A_t = \frac{1}{2}ba\)

\(126 = \frac{1}{2}ba\)

\(a = \frac{252}{b}\)

\(b = \frac{252}{b} -4\)

\(b^2 = 252 - 4b \)

\(b^2+4b- 252=0 \)

\((b-14)(b+18) = 0\)

\(b = 14\)

\(a = 14+4 = 18\)