Question

what happens to the perimeter of a triangle when it is scaled by a factor of 3?
a. it doubles
b. it triples
c. it quadruples
d. it remains the same
which field does not typically use sss similarity?
a. cartography
b. architecture
c. literature
d. engineering
in surveying, why is sss similarity useful?
a. to measure angles
b. to find the area of land
c. to verify that plots of land are similar in shape
d. to create 3d models

Explanation:

Step1: Recall perimeter - scaling relationship

Let the sides of the original triangle be $a$, $b$, and $c$, so the original perimeter $P_1=a + b + c$. When scaled by a factor of 3, the new sides are $3a$, $3b$, and $3c$.

Step2: Calculate new perimeter

The new perimeter $P_2=3a + 3b+3c = 3(a + b + c)=3P_1$. So the perimeter triples.

Step3: Analyze SSS - similarity usage

SSS (Side - Side - Side) similarity is about the proportionality of sides of triangles. Cartography, architecture, and engineering deal with geometric shapes and use SSS similarity for tasks like creating scaled - down maps, designing buildings with proportional parts, etc. Literature is about written works and does not use SSS similarity.

Step4: Understand SSS - similarity in surveying

In surveying, SSS similarity is used to verify that plots of land are similar in shape. Measuring angles uses other geometric principles, finding area is a different geometric calculation, and creating 3D models is not the main use of SSS similarity in surveying.

Answer:

1. b. It triples
2. c. Literature
3. c. To verify that plots of land are similar in shape