Question

I honestly don’t get how to solve this

Answer 1

Two other possible measure ments of AD and AE are

(a) Let AD = 4 units and AE = 6 units.

(b )Let AD = 2 units and AE = 3 units,

Explanation:

In ΔABC, given

AB = 8 units, BC = 9 units, AC = 12 units,

D is on AB and E is on AC

Now, when AD = 6 and AE = 9, both ΔABC and ΔADE are similar.

Also, DB = 8 units - 6 units = 2 units,

EC = 12 units - 9 units = 3 units

⇒
`(AD)/(DB)  = (AE)/(EC)  =  3`

To adjust the points D and E in such a way, triangles REMAIN SIMILAR.

(a) Let AD = 4 units and AE = 6 units

Then, DB = 8 units - 4 units = 4 units,

EC = 12 units - 6 units = 6 units

⇒
`(AD)/(DB)  =  (4)/(4) = 1 ,  \\ (AE)/(EC)  =    (6)/(6)   = 1`

⇒
`(AD)/(DB)  =  (AE)/(EC)  = 1`

Hence, ΔABC and ΔADE are similar.

(b) Let AD = 2 units and AE = 3 units

Then, DB = 8 units - 2 units = 6 units,

EC = 12 units - 3 units = 9 units

⇒
`(AD)/(DB)  =  (2)/(6) =  (1)/(3) ,  \\ (AE)/(EC)  =    (3)/(9)   =  \frac1}{3}`

⇒
`(AD)/(DB)  =  (AE)/(EC)  =(1)/(3)`

Hence, ΔABC and ΔADE are similar.