Answer:
Perimeter of ΔLMN = 80 units
Step-by-step explanation:
From the figure attached,
m∠K = m∠N = 58°
m∠J = m∠M = 76°
m∠I = m∠L = 46°
Therefore, ΔKJI and ΔNML are the similar triangles.
By the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
[tex]\frac{JK}{NM}= \frac{JI}{ML}= \frac{KI}{NL}[/tex]
[tex]\frac{9}{NM}= \frac{11}{27.5}= \frac{12}{30}[/tex]
[tex]\frac{9}{NM}= \frac{12}{30}[/tex]
NM = [tex]\frac{9\times 30}{12}[/tex]
NM = 22.5
Perimeter of the triangle LMN = ML + NM + NL
= 27.5 + 22.5 + 30
= 80 units
