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Answer:
JM = 20 units
Step-by-step explanation:
∵ Hexagon RSTUVW is similar to hexagon JKLMNP
∴ The corresponding sides and diagonals have a constant ratio
∴ [tex]\frac{RS}{JK}=\frac{ST}{KL}=\frac{TU}{LM}=\frac{UV}{MN}=\frac{VW}{NP}=\frac{RW}{JP}=\frac{RU}{JM}[/tex]
∵ ST = 6 units
∵ KL = 10
∴ [tex]\frac{ST}{KL}=\frac{6}{10}[/tex]
- Simplify it by dividing up and down by 2
∴ [tex]\frac{ST}{KL}=\frac{3}{5}[/tex]
∵ [tex]\frac{ST}{KL}=\frac{UR}{JM}[/tex]
∵ RU = 12 units
∴ [tex]\frac{3}{5}=\frac{12}{JM}[/tex]
- By using cross multiplication
∴ JM × 3 = 5 × 12
∴ 3 JM = 60
- Divide both sides by 3
∴ JM = 20 units
