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.

Answer 1

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"`