+9479 The ratio of their side lengths is...
\(\sqrt{\frac{192}{80}}\ =\ \sqrt{\frac{12}{5}}\ =\ \frac{\sqrt{12}}{\sqrt5}\ =\ \frac{\sqrt{12}\,\cdot\,\sqrt5}{\sqrt5\,\cdot\,\sqrt5}\ =\ \frac{\sqrt{12\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{\sqrt{2\,\cdot\,2\,\cdot\,3\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{\sqrt{2\,\cdot\,2}\,\cdot\,\sqrt{3\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{2\sqrt{15}}{5}\)
Now it is in the simplified form \(\frac{a\sqrt{b}}{c}\) where a, b, and c are integers.
a + b + c = 2 + 15 + 5 = 22
+9479 The ratio of their side lengths is...
\(\sqrt{\frac{192}{80}}\ =\ \sqrt{\frac{12}{5}}\ =\ \frac{\sqrt{12}}{\sqrt5}\ =\ \frac{\sqrt{12}\,\cdot\,\sqrt5}{\sqrt5\,\cdot\,\sqrt5}\ =\ \frac{\sqrt{12\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{\sqrt{2\,\cdot\,2\,\cdot\,3\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{\sqrt{2\,\cdot\,2}\,\cdot\,\sqrt{3\,\cdot\,5}}{\sqrt{5\,\cdot\,5}}\ =\ \frac{2\sqrt{15}}{5}\)
Now it is in the simplified form \(\frac{a\sqrt{b}}{c}\) where a, b, and c are integers.
a + b + c = 2 + 15 + 5 = 22
