Question

What are the values of a and b number 8​

Answer 1

`\large\boxed{C.\ a=(400)/(21),\ b=(580)/(21)}`

Explanation:

(LOOK AT THE PICTURE)

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

`(AB)/(AD)=(AC)/(DC)`

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

`(b)/(20)=(29)/(21)` cross multiply

`21b=(20)(29)`

`21b=580` divide both sides by 21

`b=(580)/(21)`

and in proportion:

`(BD)/(AD)=(AD)/(DC)`

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

`(a)/(20)=(20)/(21)` cross multiply

`21a=(20)(20)`

`21a=400` divide both sides by 21

`a=(400)/(21)`