The perimeters of two similar triangles ∆XYZ and ∆LMN are 48 cm and 32 cm respectively. If LM = 12 cm, then what is the length of XY?

Correct option is A

Given:

Perimeter of triangle ΔXYZ = 48 cm

Perimeter of triangle ΔLMN = 32 cm

LM = 12 cm

ΔXYZ ∼ ΔLMN (the triangles are similar)

Formula Used:

​$$\frac{\text{Perimeter of } \Delta XYZ}{\text{Perimeter of } \Delta LMN} = \frac{\text{Corresponding side of } \Delta XYZ}{\text{Corresponding side of } \Delta LMN}$$​​

Solution:

Let the length of XY be x. 

​$$\frac{48}{32} = \frac{x}{12}$$​​

​$$\frac{3}{2} = \frac{x}{12}$$​​

​$$x = \frac{3}{2} \times 12 = 18 \, \text{cm}$$​

Thus, the length of XY is 18 cm.