Step 1

Let the area of two similar triangles be \(\displaystyle{A}{1}={81}{f}{e}{e}{t}^{{2}}{\quad\text{and}\quad}{A}{2}={100}{f}{e}{e}{t}^{{2}}\)

Hence, the similarity ratio \(\displaystyle={\left({A}\frac{{1}}{{A}}{2}\right)}^{{\frac{{1}}{{2}}}}\)

Step 2

Hence, the similarity ratio \(\displaystyle={\left(\frac{{81}}{{100}}\right)}^{{\frac{{1}}{{2}}}}=\frac{{9}}{{10}}={0.9}\)

Step 3

Hence, the final answer is \(\displaystyle\frac{{9}}{{10}}\) or 0.9

Let the area of two similar triangles be \(\displaystyle{A}{1}={81}{f}{e}{e}{t}^{{2}}{\quad\text{and}\quad}{A}{2}={100}{f}{e}{e}{t}^{{2}}\)

Hence, the similarity ratio \(\displaystyle={\left({A}\frac{{1}}{{A}}{2}\right)}^{{\frac{{1}}{{2}}}}\)

Step 2

Hence, the similarity ratio \(\displaystyle={\left(\frac{{81}}{{100}}\right)}^{{\frac{{1}}{{2}}}}=\frac{{9}}{{10}}={0.9}\)

Step 3

Hence, the final answer is \(\displaystyle\frac{{9}}{{10}}\) or 0.9