Question

What are the values of a and b number 8​

Answer 1

Answer:

$\large\boxed{C.\ a=\dfrac{400}{21},\ b=\dfrac{580}{21}}$

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔABC, ΔDBA and ΔDAC are similar (AAA). Therefore the corresponding sides are in proportion:

$\dfrac{AB}{AD}=\dfrac{AC}{DC}$

We have AB = b, AD = 20, AC = 29 and DC = 21. Substitute:

$\dfrac{b}{20}=\dfrac{29}{21}$             cross multiply

$21b=(20)(29)$

$21b=580$           divide both sides by 21

$b=\dfrac{580}{21}$

and in proportion:

$\dfrac{BD}{AD}=\dfrac{AD}{DC}$

We have BD = a, AD = 20 and DC = 21. Substitute:

$\dfrac{a}{20}=\dfrac{20}{21}$           cross multiply

$21a=(20)(20)$

$21a=400$   divide both sides by 21

$a=\dfrac{400}{21}$