Question

if $jk = 11$, $kl = 10$, $jl = 12$, $no = 18$, and $mo = 21.6$, find the perimeter of $\triangle mno$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Confirm triangle similarity

Triangles $\triangle JKL$ and $\triangle MNO$ have all corresponding angles equal ($53^\circ, 59^\circ, 68^\circ$), so they are similar.

Step2: Find similarity ratio

Corresponding sides $JL = 12$ and $MO = 21.6$.
Ratio $r = \frac{MO}{JL} = \frac{21.6}{12} = 1.8$

Step3: Calculate side $MN$

Corresponding side to $JK = 11$:
$MN = JK \times r = 11 \times 1.8 = 19.8$

Step4: Calculate perimeter of $\triangle MNO$

Sum all sides: $MN + NO + MO = 19.8 + 18 + 21.6$

Answer:

59.4