Question

1. the two triangles below are similar. what is the perimeter of triangle xyz?

(image of triangle mln with ml=20 cm, ln=15 cm, mn=25 cm; and triangle xyz with xz=6 cm, other sides unknown)
handwritten notes: find s.f. then multi then add, s.f 6/15 =...

Explanation:

Step1: Find the scale factor

First, identify the corresponding sides. Side \( LN = 15 \, \text{cm} \) in triangle \( MLN \) corresponds to side \( XZ = 6 \, \text{cm} \) in triangle \( XYZ \). The scale factor \( k \) is \( \frac{XZ}{LN}=\frac{6}{15}=\frac{2}{5} \).

Step2: Find the perimeter of triangle \( MLN \)

The sides of triangle \( MLN \) are \( 20 \, \text{cm} \), \( 15 \, \text{cm} \), and \( 25 \, \text{cm} \). Its perimeter \( P_{MLN}=20 + 15+25 = 60 \, \text{cm} \).

Step3: Find the perimeter of triangle \( XYZ \)

Since the triangles are similar, the ratio of their perimeters is equal to the scale factor. Let \( P_{XYZ} \) be the perimeter of triangle \( XYZ \). Then \( \frac{P_{XYZ}}{P_{MLN}}=k \), so \( P_{XYZ}=P_{MLN}\times k = 60\times\frac{2}{5}=24 \, \text{cm} \).

Answer:

The perimeter of triangle \( XYZ \) is \( 24 \, \text{cm} \).