Question

RU and JM are diagonals. Given ST= 6, KL = 10, and RU= 12, find JM

Answer 1

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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

∴ $\frac{RS}{JK}=\frac{ST}{KL}=\frac{TU}{LM}=\frac{UV}{MN}=\frac{VW}{NP}=\frac{RW}{JP}=\frac{RU}{JM}$

∵ ST = 6 units

∵ KL = 10

∴ $\frac{ST}{KL}=\frac{6}{10}$

- Simplify it by dividing up and down by 2

∴ $\frac{ST}{KL}=\frac{3}{5}$

∵ $\frac{ST}{KL}=\frac{UR}{JM}$

∵ RU = 12 units

∴  $\frac{3}{5}=\frac{12}{JM}$

- By using cross multiplication

∴ JM × 3 = 5 × 12

∴ 3 JM = 60

- Divide both sides by 3

∴ JM = 20 units