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

5929

19177

79292

we 29t71

Answer 2

AL: DM is in the ratio 1:2

Step-by-step explanation:

Given: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE = 10 cm, EF = 8 cm and FD = 8.4 cm.  

AL⊥BC and DM⊥EF

To find: AL:DM

Solution:

Let's find the ratio of the corresponding sides in the two triangles.

AB/DE = 5/10

BC/EF = 4/8

AC/DE = 4.2/8.4

We note that the corresponding sides are all in the same proportion of 1/2.

So ΔABC ~  ΔDEF (SSS similarity)

In ΔABL ~ ΔDEF  

∠B = ∠E (corresponding angles)

∠ALB = ∠DME (90 degress)

ΔABL ~ ΔDEF  (AA similarity)

So AB/DE = AL/DM (corresponding sides)

5/10 = AL/DM

So AL: DM is in the ratio 1:2