Question

Rachel is trying to find the length of the lake shown on the diagram. She knows that if the two triangles are similar, she can use a proportion to solve for the length. How can Rachel justify that the triangles are similar? What is the length of the lake? A) Corresponding sides of the two triangles have the ratio of 4:1, which proves SAS similarity.The length of the lake is 212 m. B) Corresponding sides of the two triangles have the ratio of 4:1, which proves SSS similarity. The length of the lake is 132 m.
C) Corresponding sides of the two triangles have the ratio of 3:1, which proves SSS similarity. The length of the lake is 159 m. D)
Corresponding sides of the two triangles have the ratio of 4:1, which proves AAS similarity. The length of the lake is 240 m.

Answer 1

Answer: B) Corresponding sides of the two triangles have the ratio of 4:1, which proves SSS similarity. The length of the lake is 132m.

Step-by-step explanation: Similar Triangles are triangles with corresponding sides proportional to each other.

One way to determine if two triangles are similar is a theorem called Side-Side-Side Similarity Theorem or SSS similarity and it states that two triangles are similar if corresponding angles are equal and corresponding sides are proportional.

The triangles below are similar and they obey this theorem because we observe that the angles are the same and the corresponding sides are proportional:

$\frac{big}{small}=\frac{212}{53}=\frac{60}{15}=4$

So, the ratio of bigger triangle and smaller triangle is 4:1.

With that ratio and suppose length is represented as L:

$\frac{L}{33} =4$

L = 132

The length of the lake is 132m.

Thus, the answer for this question is

1) The similarity of the triangles is proved by SSS similarty;

2) Ratio of proportion is 4:1;

3) Length of the lake is 132m;