Answer:
[tex]\large\boxed{C.\ a=\dfrac{400}{21},\ b=\dfrac{580}{21}}[/tex]
Step-by-step explanation:
(LOOK AT THE PICTURE)
ΔABC, ΔDBA and ΔDAC are similar (AAA). Therefore the corresponding sides are in proportion:
[tex]\dfrac{AB}{AD}=\dfrac{AC}{DC}[/tex]
We have AB = b, AD = 20, AC = 29 and DC = 21. Substitute:
[tex]\dfrac{b}{20}=\dfrac{29}{21}[/tex] cross multiply
[tex]21b=(20)(29)[/tex]
[tex]21b=580[/tex] divide both sides by 21
[tex]b=\dfrac{580}{21}[/tex]
and in proportion:
[tex]\dfrac{BD}{AD}=\dfrac{AD}{DC}[/tex]
We have BD = a, AD = 20 and DC = 21. Substitute:
[tex]\dfrac{a}{20}=\dfrac{20}{21}[/tex] cross multiply
[tex]21a=(20)(20)[/tex]
[tex]21a=400[/tex] divide both sides by 21
[tex]a=\dfrac{400}{21}[/tex]
