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Question
In ΔABC and ΔDEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE=10cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL: DM.
Solution
Since, `"AB"/"DE"="BC"/"EF"="AC"/"DE"=1/2`
Then, ΔABC ~ ΔDEF [By SSS similarity]
Now, In ΔABL ~ ΔDEM
∠B = ∠E [Δ ABC ~ ΔDEF]
∠ALB = ∠DME [Each 90°]
Then, ΔABL ~ ΔDEM [By AA similarity]
`therefore"AB"/"DE"="AL"/"DM"` [Corresponding parts of similar Δ are proportional]
`rArr5/10="AL"/"DM"`
`rArr1/2="AL"/"DM"`
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