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
⇒[tex]\frac{AD}{DB} = \frac{AE}{EC} = 3[/tex]
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
⇒[tex]\frac{AD}{DB} = \frac{4}{4} = 1 , \\ \frac{AE}{EC} = \frac{6}{6} = 1[/tex]
⇒[tex]\frac{AD}{DB} = \frac{AE}{EC} = 1[/tex]
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
⇒[tex]\frac{AD}{DB} = \frac{2}{6} = \frac{1}{3} , \\ \frac{AE}{EC} = \frac{3}{9} = \frac1}{3}[/tex]
⇒[tex]\frac{AD}{DB} = \frac{AE}{EC} =\frac{1}{3}[/tex]
Hence, ΔABC and ΔADE are similar.
