Question

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

Answer 1

Answer:

a = 4.5 units

b = 7.5 units

Step-by-step explanation:

By using mean proportional theorem in the ΔACB,

ΔACB ~ ΔADC ~ ΔCDB

$\frac{AD}{CD}=\frac{CD}{DB}$

$\frac{8}{6}=\frac{6}{a}$

a = $\frac{6\times 6}{8}$

a = 4.5

$\frac{AB}{CB}=\frac{CB}{DB}$

$\frac{(a+8)}{b}=\frac{b}{a}$

Since a = 4.5

$\frac{4.5+8}{b}=\frac{b}{4.5}$

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.