Question

If JK = 9, KI = 12, JI = 11, NL = 30, and ML = 27.5, find the perimeter of LMN. Round your answer to the nearest tenth if necessary. Figures are not
necessarily drawn to scale.

Answer 1

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"

$\frac{JK}{NM}= \frac{JI}{ML}= \frac{KI}{NL}$

$\frac{9}{NM}= \frac{11}{27.5}= \frac{12}{30}$

$\frac{9}{NM}= \frac{12}{30}$

NM = $\frac{9\times 30}{12}$

NM = 22.5

Perimeter of the triangle LMN = ML + NM + NL

                                                  =  27.5 + 22.5 + 30

                                                  = 80 units