Solve {l}{abpi=12pi}{a/c=frac{sqrt{7}}{4}}{a^2=b^2+c^2}

$$\left\{ \begin{array} { l } { a b \pi = 12 \pi } \\ { \frac { a } { c } = \frac { \sqrt { 7 } } { 4 } } \\ { a ^ { 2 } = b ^ { 2 } + c ^ { 2 } } \end{array} \right.$$

Solve for a, b, c

$$a=\sqrt{2}\sqrt[4]{7}\left(1+i\right)\approx 2.300326634+2.300326634i\text{, }b=\sqrt{2}\times 7^{\frac{3}{4}}\left(\frac{3}{7}-\frac{3}{7}i\right)\approx 2.608325232-2.608325232i\text{, }c=\sqrt{2}\times 7^{\frac{3}{4}}\left(\frac{4}{7}+\frac{4}{7}i\right)\approx 3.477766976+3.477766976i$$

$$a=\sqrt{2}\sqrt[4]{7}\left(-1+i\right)\approx -2.300326634+2.300326634i\text{, }b=\sqrt{2}\times 7^{\frac{3}{4}}\left(-\frac{3}{7}-\frac{3}{7}i\right)\approx -2.608325232-2.608325232i\text{, }c=\sqrt{2}\times 7^{\frac{3}{4}}\left(-\frac{4}{7}+\frac{4}{7}i\right)\approx -3.477766976+3.477766976i$$

$$a=\sqrt{2}\sqrt[4]{7}\left(-1-i\right)\approx -2.300326634-2.300326634i\text{, }b=\sqrt{2}\times 7^{\frac{3}{4}}\left(-\frac{3}{7}+\frac{3}{7}i\right)\approx -2.608325232+2.608325232i\text{, }c=\sqrt{2}\times 7^{\frac{3}{4}}\left(-\frac{4}{7}-\frac{4}{7}i\right)\approx -3.477766976-3.477766976i$$

$$a=\sqrt{2}\sqrt[4]{7}\left(1-i\right)\approx 2.300326634-2.300326634i\text{, }b=\sqrt{2}\times 7^{\frac{3}{4}}\left(\frac{3}{7}+\frac{3}{7}i\right)\approx 2.608325232+2.608325232i\text{, }c=\sqrt{2}\times 7^{\frac{3}{4}}\left(\frac{4}{7}-\frac{4}{7}i\right)\approx 3.477766976-3.477766976i$$