Question

In 𝚫𝑨𝑩𝑪 and 𝚫𝑫𝑬𝑭, it is being given that 𝑨𝑩 = 𝟓 𝒄𝒎, 𝑩𝑪 = 𝟒 𝒄𝒎 and 𝑪𝑨 = 𝟒.𝟐 𝒄𝒎, 𝑫𝑬=𝟏𝟎 𝒄𝒎, 𝑬𝑭 = 𝟖 𝒄𝒎 and 𝑭𝑫 = 𝟖.𝟒 𝒄𝒎. If 𝑨𝑳 ⊥ 𝑩𝑪 and 𝑫𝑴 ⊥ 𝑬𝑭, find 𝑨𝑳/𝑫𝑴.

Answer 1

Since,
𝐴𝐵/𝐷𝐸 = 𝐵𝐶/𝐸𝐹 = 𝐴𝐶/𝐷F = 1/2
Then, ΔABC ~ ΔDEF [By SSS similarity]
Now, In ΔABL and ΔDEM
∠B = ∠E [Δ ABC ~ ΔDEF]
∠ALB = ∠DME [Each 90°]
Then, ΔABL ~ ΔDEM [By AA similarity]
∴ 𝐴𝐵/𝐷𝐸 = 𝐴𝐿/𝐷𝑀
[Corresponding parts of similar triangles are proportional]
⇒ 5/10 = 𝐴𝐿/𝐷𝑀
⇒1/2 = 𝐴𝐿/DM