Given:
There are given two triangles, KIJ and LMN.
Where,
[tex]\begin{gathered} JK=76 \\ KI=40 \\ JI=55 \\ NL=36 \\ ML=49.5 \end{gathered}[/tex]
Explanation:
To find the perimeter of triangle LMN, first, find the missing sides of this triangle.
Then,
We can see that the side ML and NL are given but side MN is missing.
So,
For MN:
[tex]\frac{KI}{NL}=\frac{JK}{MN}[/tex]
Then,
[tex]\begin{gathered} \frac{KI}{NL}=\frac{JK}{MN} \\ \frac{40}{36}=\frac{76}{MN} \\ 40\times MK=76\times30 \\ MN=\frac{76\times30}{40} \\ MN=57 \end{gathered}[/tex]
Now,
From the formula of the perimeter of the triangle LMN :
[tex]P=LM+MN+NL[/tex]
Then,
[tex]\begin{gathered} P=LM+MN+NL \\ P=49.5+57+36 \\ P=142.5 \end{gathered}[/tex]
