Question

Use similar triangles and a proportion to find the length of the lake shown here.
​(Hint: The side 70 m long in the smaller triangle corresponds to side of 70 m plus 90 m equals 160 m in the larger​ triangle.)
70 m
90 m
160 m
35 m
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Part 1
nequals
  
enter your response here m

Answer 1

To find the length of the lake using similar triangles and proportions, we can set up a proportion based on the corresponding sides of the triangles.

1. Identify the sides:
- In the smaller triangle, we have:
- Side A = 70 m (side corresponding to the larger triangle's side of 160 m)
- Side B = 35 m (the unknown side we are trying to find)

- In the larger triangle, we have:
- Side corresponding to 70 m (the smaller triangle) = 160 m
- The side corresponding to 35 m (the unknown) is what we are trying to find, let's call it \( x \).

2. Set up the proportion based on the relationship of the sides of the similar triangles:
\[
\frac{70 m}{160 m} = \frac{35 m}{x}
\]

3. Cross-multiply to solve for \( x \):
\[
70 m \cdot x = 35 m \cdot 160 m
\]
\[
70x = 5600
\]

4. Now divide both sides by 70 to find \( x \):
\[
x = \frac{5600}{70} = 80
\]

Thus, the length of the lake \( n \) equals **80 m**.