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

Question
Similarity
Solve for LM. Hint: Read your similarity statement. Set up a proportion, and solve for $$\displaystyle\times$$ first.

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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