Question

I honestly don’t get how to solve this

Answer 1

Answer:

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,

Step-by-step 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

⇒$\frac{AD}{DB} = \frac{AE}{EC} = 3$

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

⇒$\frac{AD}{DB} = \frac{4}{4} = 1 , \\ \frac{AE}{EC} = \frac{6}{6} = 1$

⇒$\frac{AD}{DB} = \frac{AE}{EC} = 1$

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

⇒$\frac{AD}{DB} = \frac{2}{6} = \frac{1}{3} , \\ \frac{AE}{EC} = \frac{3}{9} = \frac1}{3}$

⇒$\frac{AD}{DB} = \frac{AE}{EC} =\frac{1}{3}$

Hence,   ΔABC and ΔADE are similar.