Question

Geometry math question no Guessing and Please show work

Answer 1

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: $\frac{60m}{L}$ = $\frac{20 m }{70 m}$ ;

Note: " $\frac{20m}{70m}$ = $\frac{2}{7}$ ;

Rewrite as:

$\frac{60m}{L}$ = $\frac{2}{7}$ .

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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