Question

What is the value of A and B and if you can please show how you got that answer

Answer 1

a = 4.5 units

b = 7.5 units

Explanation:

By using mean proportional theorem in the ΔACB,

ΔACB ~ ΔADC ~ ΔCDB

`(AD)/(CD)=(CD)/(DB)`

`(8)/(6)=(6)/(a)`

a =
`(6* 6)/(8)`

a = 4.5

`(AB)/(CB)=(CB)/(DB)`

`((a+8))/(b)=(b)/(a)`

Since a = 4.5

`(4.5+8)/(b)=(b)/(4.5)`

b² = 4.5 × 12.5

b = √56.25

b = 7.5 units

Therefore, a = 4.5 units and b = 7.5 units will be the answer.