Question

What is the length of AB?

Answer 1

AB = 7.35 cm

Explanation:

From the attachment,

In ΔDEF,

DF = GH-(GD+FH) = 6 - (2+3) = 1 cm

DE = 2+3 = 5 cm (sum of two radius)

Applying Pythagoras theorem,

`EF=√(DE^2-DF^2)=√(5^2-1^2)=√(24)=2\sqrt6`

In ΔCDI,

DI = GH-(GD+IH) = 6 - (2+1.5) = 2.5 cm

CD = 2+1.5 = 3.5 cm (sum of two radius)

Applying Pythagoras theorem,

`CI=√(CD^2-DI^2)=√(3.5^2-2.5^2)=\sqrt6`

AB = EF + CI =
`2\sqrt6+\sqrt6=3\sqrt6=7.35\ cm`