Question

question 4
triangles pqr and pst are similar to each other. find the scale factor.
image of two similar triangles with labeled sides: pt has segments tr=4 cm and rp=2 cm; ps has segments pq=4 cm and qs=8 cm
options: 3, 4, 5, 6

Explanation:

Step1: Identify corresponding sides

For similar triangles \( \triangle PQR \) and \( \triangle PST \), we can take the vertical sides \( PR \) and \( PT \), or horizontal sides \( PQ \) and \( PS \).
\( PR = 2 \, \text{cm} \), \( PT = PR + RT = 2 + 4 = 6 \, \text{cm} \) (or \( PQ = 4 \, \text{cm} \), \( PS = PQ + QS = 4 + 8 = 12 \, \text{cm} \)).

Step2: Calculate scale factor

Scale factor is the ratio of corresponding sides of the larger triangle to the smaller one.
Using vertical sides: \( \frac{PT}{PR} = \frac{6}{2} = 3 \).
(Or using horizontal sides: \( \frac{PS}{PQ} = \frac{12}{4} = 3 \).)

Answer:

3