Question

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

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asked 2021-02-12
Find the similarity ratio of two triangles with areas \(\displaystyle{81}{f}{e}{e}{t}^{{2}}{\quad\text{and}\quad}{100}{f}{e}{e}{t}^{{2}}\).

Answers (1)

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
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