The answer is: [C]: " 210 m " .
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The distance across the lake is: " 210 m " .
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Explanation: To solve:
Assume that: "L" represents the distance across the lake, in units of "m" ("meters").
We are given: "Assume the triangles are similar".
So; let us assume that: "60 m" is similar to "L" .
"x" is similar to "y" .
"20 m " is similar to "70 m".
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So: [tex] \frac{60m}{L} [/tex] = [tex] \frac{20 m }{70 m} [/tex] ;
Note: " [tex] \frac{20m}{70m} [/tex] = [tex] \frac{2}{7} [/tex] ;
Rewrite as:
[tex] \frac{60m}{L} [/tex] = [tex] \frac{2}{7} [/tex] .
Now, cross multiply:
2L = 7 * 60m ;
→ 2L = 420m ;
Divide each side of the equation by "2" ;
to isolate "L" on one side of the equation; & to solve for "L" ;
→ 2L / 2 = 420m / 2 ;
to get:
→ L = 210 m .
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The answer is: " 210 m " .
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which corresponds to:
Answer choice: [C]: " 210 m " .
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