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Solve for LM. Hint: Read your similarity statement. Set up a proportion, and solve for xx first.12210107041.jpg

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asked 2020-11-17

Solve for LM. Hint: Read your similarity statement. Set up a proportion, and solve for \(\displaystyle\times\) first.
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Answers (1)

2020-11-18
Step 1
Two triangles are similar if the lenght of corrspanding sides are proportional.
Step 2
\(\displaystyle\triangle{P}{M}{L}\sim\triangle{T}{R}{Q}\)
\(\displaystyle\Rightarrow\frac{{{P}{M}}}{{{T}{R}}}=\frac{{{M}{L}}}{{{R}{Q}}}\)
\(\displaystyle\Rightarrow\frac{{{15}}}{{{14}}}=\frac{{{7}{x}-{9}}}{{{2}{x}+{2}}}\)
\(\displaystyle\Rightarrow{35}{\left({2}{x}+{2}\right)}={14}{\left({7}{x}-{9}\right)}\)
\(\displaystyle\Rightarrow{70}{x}+{70}={98}{x}-{126}\)
\(\displaystyle\Rightarrow{70}+{126}={98}{x}-{70}{x}\)
\(\displaystyle\Rightarrow{196}={28}{x}\)
\(\displaystyle\Rightarrow{x}=\frac{{196}}{{28}}={7}\)
Step 3
Now
\(\displaystyle{L}{M}={7}{x}-{9}\)
\(\displaystyle{L}{M}={7}{\left({7}\right)}-{9}\)
\(\displaystyle{L}{M}={40}\)
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