Question

# Find the similarity ratio of two triangles with areas 81 feet^2 and 100 feet^2.

Similarity
Find the similarity ratio of two triangles with areas $$\displaystyle{81}{f}{e}{e}{t}^{{2}}{\quad\text{and}\quad}{100}{f}{e}{e}{t}^{{2}}$$.

2021-02-13
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